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Author ID: laptev.ari Recent zbMATH articles by "Laptev, Ari"
Published as: Laptev, Ari; Laptev, A.; Laptev, A. A.; Laptev, Ari A.
Further Spellings: Laptev, Ari Arievich
Homepage: http://wwwf.imperial.ac.uk/~alaptev/
External Links: MGP · Wikidata · Google Scholar · Math-Net.Ru · dblp · GND · IdRef · theses.fr
Documents Indexed: 126 Publications since 1974
11 Contributions as Editor
Biographic References: 3 Publications
Co-Authors: 107 Co-Authors with 111 Joint Publications
3,452 Co-Co-Authors
all top 5

Co-Authors

25 single-authored
11 Naboko, Serguei N.
10 Safronov, Oleg
9 Ilyin, Alexei A.
8 Dolbeault, Jean
8 Esteban, Maria J.
8 Loss, Michael
8 Safarov, Yuri G.
7 Birman, Mikhail Shlëmovich
7 Frank, Rupert L.
7 Kurasov, Pavel B.
6 Weidl, Timo
5 Hoffmann-Ostenhof, Thomas
5 Solomyak, Mikhaĭl Zakharovich
5 Zelik, Sergey V.
4 Janas, Jan
4 Kovařík, Hynek
4 Suslina, Tat’yana Aleksandrovna
3 Schimmer, Lukas
3 Simon, Barry
3 Sobolev, Alexander V.
3 Stolz, Gunter
3 Yafaev, Dimitri R.
2 Bonheure, Denis
2 Dittrich, Jaroslav
2 Faddeev, Lyudvig Dmitrievich
2 Ferrulli, Francesco
2 Gesztesy, Fritz
2 Guzu, Dorian
2 Hoffmann-Ostenhof, Maria
2 Kapitanski, Lev
2 Korotyaev, Evgeny L.
2 Mitrea, Marius
2 Molchanov, Stanislav Alekseevich
2 Östensson, Jörgen
2 Seiringer, Robert
2 Shterenberg, Roman G.
2 Sukhtaiev, Selim
2 Takhtajan, Leon Armenovich
2 Ural’tseva, Nina Nikolaevna
2 Vasil’ev, Dimitri G.
2 Velicu, Andrei
2 Vershik, Anatoliĭ Moiseevich
1 Aermark, L.
1 Aksent’ev, Leonid Aleksandrovich
1 Aptekarev, Alexander Ivanovich
1 Ashbaugh, Mark S.
1 Avkhadiev, Farit Gabidinovich
1 Babich, Vasiliĭ Mikhaĭlovich
1
1 Bikchentaev, Aĭrat Midkhatovich
1 Bourguignon, Jean-Pierre
1 Bühlmann, Peter
1 Buslaev, Vladimir Savel’evich
1 Chanillo, Sagun
1 Cuenin, Jean-Claude
1 Dubinin, Vladimir N.
1 Ekholm, Tomas
1 Elizarov, A. M.
1 Exner, Pavel
1 Fanelli, Luca
1 Fedotov, Alexander
1 Geisinger, Leander
1 Gindikin, Simon Grigorevich
1 Glushkin, E. D.
1 Gordon, Alexander Ya.
1 Goryainov, Viktor V.
1 Hansson, Anders M.
1 Hassannezhad, Asma
1 Khavin, Viktor Petrovich
1 Helffer, Bernard
1 Hundertmark, Dirk
1 Its, Alexander Rudolfovich
1 Kayumov, Il’giz Rifatovich
1 Kislyakov, Sergeĭ Vital’evich
1 Krejčiřík, David
1 Langmann, Edwin
1 Levitin, Michael R.
1 Lieb, Elliott Hershel
1 Maad Sasane, Sara
1 Makarov, Boris Mikhaĭlovich
1 Marchenko, Vladimir Aleksandrovich
1 Mityagin, Boris Samuilovich
1 Nasyrov, Semen R.
1 Natalini, Roberto
1 Nevai, Paul G.
1 Nikol’skiĭ, Nikolaĭ Kapitonovich
1 Pastur, Leonid Andreevich
1 Paufler, Cornelius
1 Peicheva, Anastasiya S.
1 Plamenevskiĭ, Boris Alekseevich
1 Portmann, Fabian
1 Prokhorov, Dmitriĭ Vladimirovich
1 Robert, Didier
1 Rozenblum, Grigori V.
1 Ruzhansky, Michael V.
1 Salinger, David L.
1 Sergeev, Armen Glebovich
1 Shlapunov, Aleksandr Anatol’evich
1 Sigal, Israel Michael
1 Stepanov, Vladimir Dmitrievich
...and 8 more Co-Authors
all top 5

Serials

8 Journal of Functional Analysis
6 Communications in Mathematical Physics
5 St. Petersburg Mathematical Journal
5 Operator Theory: Advances and Applications
4 Russian Mathematical Surveys
3 Journal of Mathematical Physics
3 Functional Analysis and its Applications
3 Journal of the London Mathematical Society. Second Series
3 IMRN. International Mathematics Research Notices
3 Journal of Mathematical Sciences (New York)
3 Problemy Matematicheskogo Analiza
3 European Mathematical Society Newsletter
3 Journal of Spectral Theory
2 Communications on Pure and Applied Mathematics
2 Mathematical Notes
2 Arkiv för Matematik
2 Reviews in Mathematical Physics
2 Proceedings of the American Mathematical Society
2 Annales Henri Poincaré
2 Analysis and Mathematical Physics
2 Bulletin of Mathematical Sciences
1 Inverse Problems
1 Journal of Mathematical Analysis and Applications
1 Journal of Statistical Physics
1 Letters in Mathematical Physics
1 Matematicheskie Zametki
1 Nonlinearity
1 Acta Mathematica
1 Advances in Mathematics
1 Gazette des Mathématiciens
1 Inventiones Mathematicae
1 Journal of Soviet Mathematics
1 Mathematische Nachrichten
1 Mathematica Scandinavica
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Soviet Mathematics. Doklady
1 Transactions of the Moscow Mathematical Society
1 Trudy Moskovskogo Matematicheskogo Obshchestva
1 Asymptotic Analysis
1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
1 Geometric and Functional Analysis. GAFA
1 Communications in Partial Differential Equations
1 Journal of Physics A: Mathematical and General
1 Mathematical Research Letters
1 Sbornik: Mathematics
1 Doklady Mathematics
1 Journal of the European Mathematical Society (JEMS)
1 Communications in Contemporary Mathematics
1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
1 Journal of Mathematical Physics, Analysis, Geometry
1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
1 Complex Variables and Elliptic Equations
1 Complex Analysis and Operator Theory
1 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova
1 Analysis & PDE
1 Wiadomości Matematyczne
1 Pure and Applied Functional Analysis
1 EMS Series of Congress Reports

Publications by Year

Citations contained in zbMATH Open

94 Publications have been cited 1,023 times in 648 Documents Cited by Year
Sharp Lieb-Thirring inequalities in high dimensions. Zbl 1142.35531
Laptev, Ari; Weidl, Timo
72
2000
Hardy inequalities for magnetic Dirichlet forms. Zbl 0977.26005
Laptev, Ari; Weidl, Timo
61
1999
Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces. Zbl 0892.35115
Laptev, A.
60
1997
A geometrical version of Hardy’s inequality. Zbl 1012.26011
Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Laptev, A.
50
2002
Eigenvalue estimates for Schrödinger operators with complex potentials. Zbl 1185.35045
Laptev, Ari; Safronov, Oleg
50
2009
Recent results on Lieb-Thirring inequalities. Zbl 1135.81337
Laptev, Ari; Weidl, Timo
44
2000
Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382
Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert
44
2006
Lieb-Thirring inequalities with improved constants. Zbl 1152.35451
Dolbeault, Jean; Laptev, Ari; Loss, Michael
33
2008
The negative discrete spectrum of a two-dimensional Schrödinger operator. Zbl 0864.35080
Birman, M. Sh.; Laptev, A.
26
1996
New bounds on the Lieb-Thirring constants. Zbl 1074.35569
Hundertmark, D.; Laptev, A.; Weidl, T.
25
2000
On new relations between spectral properties of Jacobi matrices and their coefficients. Zbl 1135.47303
Laptev, A.; Naboko, S.; Safronov, O.
25
2003
On the number of eigenvalues of Schrödinger operators with complex potentials. Zbl 1358.35074
Frank, Rupert L.; Laptev, Ari; Safronov, Oleg
24
2016
One-dimensional Gagliardo-Nirenberg-Sobolev inequalities: remarks on duality and flows. Zbl 1320.26017
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
23
2014
Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials. Zbl 1077.81040
Laptev, A.; Naboko, S.; Safronov, O.
23
2005
Eigenvalue estimates for non-selfadjoint Dirac operators on the real line. Zbl 1287.81050
Cuenin, Jean-Claude; Laptev, Ari; Tretter, Christiane
22
2014
Hardy inequalities for nonconvex domains. Zbl 1183.26017
Avkhadiev, Farit; Laptev, Ari
21
2010
Weyl type asymptotics and bounds for the eigenvalues of functional-difference operators for mirror curves. Zbl 1361.47004
Laptev, Ari; Schimmer, Lukas; Takhtajan, Leon A.
19
2016
Szegö type limit theorems. Zbl 0878.47020
Laptev, A.; Safarov, Yu.
17
1996
Generalized Hardy inequality for the magnetic Dirichlet forms. Zbl 1127.26015
Balinsky, Alexander; Laptev, Ari; Sobolev, Alexander V.
17
2004
Spectral estimates on the sphere. Zbl 1293.35183
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari
16
2014
Geometrical versions of improved Berezin-Li-Yau inequalities. Zbl 1257.35138
Geisinger, Leander; Laptev, Ari; Weidl, Timo
16
2011
Many-particle Hardy inequalities. Zbl 1135.35012
Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Laptev, A.; Tidblom, J.
15
2008
A sharp bound on eigenvalues of Schrödinger operators on the half-line with complex-valued potentials. Zbl 1253.35086
Frank, Rupert L.; Laptev, Ari; Seiringer, Robert
15
2011
Global Fourier integral operators and semiclassical asymptotics. Zbl 0962.35201
Laptev, A.; Sigal, I. M.
14
2000
Discrete spectrum of the perturbed Dirac operator. Zbl 0822.35104
Birman, Mikhail Sh.; Laptev, Ari
13
1994
Nonlinear eigenvalues and analytic hypoellipticity. Zbl 1053.35045
Chanillo, Sagun; Helffer, Bernard; Laptev, Ari
12
2004
Spectral properties of Schrödinger operators on compact manifolds: rigidity, flows, interpolation and spectral estimates. Zbl 1276.58007
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
10
2013
Hardy inequalities for Robin Laplacians. Zbl 1242.26022
Kovařík, Hynek; Laptev, Ari
10
2012
On the negative spectrum of the two-dimensional Schrödinger operator with radial potential. Zbl 1253.35037
Laptev, A.; Solomyak, M.
10
2012
Hardy inequalities with homogeneous weights. Zbl 1322.35103
Hoffmann-Ostenhof, Thomas; Laptev, Ari
10
2015
On the eigenvalue behaviour for a class of differential operators on the semiaxis. Zbl 0916.34067
Birman, M. Sh.; Laptev, A.; Solomyak, M.
9
1998
The negative discrete spectrum of the operator \((-\Delta)^ l-\alpha V\) in \(L_ 2(\mathbb{R}^ d)\) for \(d\) even and \(2l\geq d\). Zbl 0876.35079
Birman, Mikhail Sh.; Laptev, Ari; Solomyak, Michael
9
1997
On spectral estimates for two-dimensional Schrödinger operators. Zbl 1294.35048
Laptev, Ari; Solomyak, Michael
9
2013
Trace formulae for Schrödinger operators with complex-valued potentials on cubic lattices. Zbl 1403.39017
Korotyaev, Evgeny; Laptev, Ari
8
2018
One-dimensional interpolation inequalities, Carlson-Landau inequalities, and magnetic Schrödinger operators. Zbl 1336.35016
Ilyin, Alexei; Laptev, Ari; Loss, Michael; Zelik, Sergey
8
2016
On global representations of Lagrangian distributions and solutions of hyperbolic equations. Zbl 0811.35177
Laptev, A.; Safarov, Yu.; Vassiliev, D.
8
1994
Hardy inequalities for simply connected planar domains. Zbl 1168.26003
Laptev, Ari; Sobolev, Alexander V.
8
2008
A Szegő condition for a multidimensional Schrödinger operator. Zbl 1135.35355
Laptev, A.; Naboko, S.; Safronov, O.
7
2005
Bound state asymptotics for elliptic operators with strongly degenerated symbols. Zbl 1045.35049
Laptev, Ari; Safronov, Oleg; Weidl, Timo
7
2002
On the negative eigenvalues of a class of Schrödinger operators. Zbl 0941.35055
Laptev, A.; Netrusov, Yu.
7
1999
A generalization of the Berezin-Lieb inequality. Zbl 0868.47016
Laptev, A.; Safarov, Yu.
6
1996
Solitons and the removal of eigenvalues for fourth-order differential operators. Zbl 1123.34067
Hoppe, J.; Laptev, A.; Östensson, J.
6
2006
Hardy inequalities for a magnetic Grushin operator with Aharonov-Bohm type magnetic field. Zbl 1238.35014
Aermark, L.; Laptev, Ari
6
2012
Spectral inequalities for Schrödinger operators with surface potentials. Zbl 1170.35486
Frank, Rupert L.; Laptev, Ari
6
2008
On the Lieb-Thirring conjecture for a class of potentials. Zbl 0938.35112
Laptev, Ari
5
1999
Hardy inequalities for \(p\)-Laplacians with Robin boundary conditions. Zbl 1360.47008
Ekholm, Tomas; Kovařík, Hynek; Laptev, Ari
5
2015
Magnetic rings. Zbl 1390.81142
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
5
2018
Spectral asymptotics of a certain class of Fourier integral operators. Zbl 0503.47044
Laptev, A. A.
5
1981
Eigenvalue estimates for magnetic Schrödinger operators in domains. Zbl 1186.35119
Frank, Rupert L.; Laptev, Ari; Molchanov, Stanislav
5
2008
Sharp spectral inequalities for the Heisenberg Laplacian. Zbl 1157.58008
Hansson, A. M.; Laptev, Ari
5
2008
On some sharp spectral inequalities for Schrödinger operators on semiaxis. Zbl 1297.35155
Exner, Pavel; Laptev, Ari; Usman, Muhammad
5
2014
On an estimate of the remainder term in formulas of the spectral asymptotics for one class of integral operators. Zbl 0443.47051
Laptev, A. A.
4
1977
Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. Zbl 1198.35161
Frank, Rupert L.; Laptev, Ari
4
2010
Lieb-Thirring inequalities on the torus. Zbl 1365.35096
Ilyin, Alexei A.; Laptev, Ari A.
4
2016
The negative spectrum of a class of two-dimensional Schrödinger operators with potentials depending only on radius. Zbl 0972.35079
Laptev, A.
4
2000
Discrete spectrum of the perturbed Dirac operator. Zbl 0858.47004
Birman, M. Sh.; Laptev, A.
4
1994
A bound for the eigenvalue counting function for Krein-von Neumann and Friedrichs extensions. Zbl 1362.35197
Ashbaugh, Mark S.; Gesztesy, Fritz; Laptev, Ari; Mitrea, Marius; Sukhtaiev, Selim
3
2017
Remarks on the paper of V. Guillemin and K. Okikiolu: “Subprincipal terms in Szegő estimates”. Zbl 0917.58046
Laptev, A.; Robert, D.; Safarov, Yu.
3
1998
Finding eigenvalues and eigenfunctions of the Zaremba problem for the circle. Zbl 1367.47052
Laptev, Ari; Peicheva, Anastasiya; Shlapunov, Alexander
3
2017
Interpolation inequalities and spectral estimates for magnetic operators. Zbl 1388.81104
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
3
2018
Asymptotics of the negative discrete spectrum of a class of Schrödinger operators with large coupling constant. Zbl 0795.35071
Laptev, Ari
3
1993
Symmetry results in two-dimensional inequalities for Aharonov-Bohm magnetic fields. Zbl 1439.81049
Bonheure, Denis; Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
3
2020
Spectral inequalities for partial differential equations and their applications. Zbl 1269.35050
Laptev, Ari
3
2012
On the improvement of the Hardy inequality due to singular magnetic fields. Zbl 1450.35011
Fanelli, Luca; Krejčiřík, David; Laptev, Ari; Vega, Luis
3
2020
Inverse spectral problems for Schrödinger operators with energy depending potentials. Zbl 1146.35095
Laptev, A.; Shterenberg, R.; Sukhanov, V.
2
2007
On estimates of singular numbers for a class of integral operators. Zbl 0478.47032
Laptev, A. A.
2
1981
Trace formulas for a discrete Schrödinger operator. Zbl 06835370
Korotyaev, E. L.; Laptev, A.
2
2017
On continuous and discrete Hardy inequalities. Zbl 1368.35010
Kapitanski, Lev; Laptev, Ari
2
2016
Spectral asymptotics of a class of Fourier integral operators. Zbl 0535.47030
Laptev, A. A.
2
1983
Reflectionless potentials for an ordinary differential operator of order four. Zbl 1103.34071
Laptev, A.; Shterenberg, R.; Sukhanov, V.; Östensson, J.
2
2006
Discrete spectrum of a two-dimensional periodic elliptic second order operator perturbed by a decaying potential. I: Semibounded gap. Zbl 1070.47041
Birman, M. Sh.; Laptev, A.; Suslina, T. A.
2
2001
The negative discrete spectrum of a class of two-dimensional Schrödinger operators with magnetic fields. Zbl 1083.35070
Laptev, A.; Safronov, O.
2
2005
Spectral properties of the logarithmic Laplacian. Zbl 1476.35153
Laptev, Ari; Weth, Tobias
2
2021
Spectral asymptotic behavior of a class of integral operators. Zbl 0322.45003
Laptev, A. A.
2
1975
Hardy inequalities for Landau Hamiltonian and for Baouendi-Grushin operator with Aharonov-Bohm type magnetic field. I. Zbl 1428.26029
Laptev, Ari; Ruzhansky, Michael; Yessirkegenov, Nurgissa
2
2019
Eigenvalues of the bilayer graphene operator with a complex valued potential. Zbl 1429.81034
Safronov, Oleg; Laptev, Ari; Ferrulli, Francesco
2
2019
Weyl asymptotics for perturbed functional difference operators. Zbl 1427.81063
Laptev, Ari; Schimmer, Lukas; Takhtajan, Leon A.
2
2019
Error estimate in the generalized Szegö theorem. Zbl 0743.58032
Laptev, A.; Safarov, Yu.
1
1991
Spectral asymptotics of a composition of pseudodifferential operators and reflections from the boundary. Zbl 0391.47035
Laptev, A. A.
1
1977
Around the research of Vladimir Maz’ya. II. Partial differential equations. Zbl 1180.47002
1
2010
A bound for the eigenvalue counting function for higher-order Krein Laplacians on open sets. Zbl 1339.35202
Gesztesy, F.; Mitrea, M.; Sukhtaiev, S.; Laptev, A.
1
2015
Perturbations of embedded eigenvalues for a magnetic Schrödinger operator on a cylinder. Zbl 1355.81085
Laptev, Ari; Maad Sasane, Sara
1
2017
“Non-standard” spectral asymptotics for a two-dimensional Schrödinger operator. Zbl 0910.35086
Birman, Mikhail Sh.; Laptev, Ari
1
1997
Mikhail Shlemovich Birman (obituary). Zbl 1219.01025
Babich, V. M.; Buslaev, V. S.; Vershik, A. M.; Gindikin, S. G.; Kislyakov, S. V.; Laptev, A.; Marchenko, V. A.; Nikol’skii, N. K.; Pastur, L. A.; Plamenevskii, B. A.; Solomyak, M. Z.; Suslina, T. A.; Ural’tseva, N. N.; Faddeev, L. D.; Khavin, V. P.; Yafaev, D. R.
1
2010
Operator methods in mathematical physics. Conference on operator theory, analysis and mathematical physics (OTAMP) 2010, Bedlewo, Poland. Zbl 1257.00017
1
2013
On inequalities for the bound states of Schrödinger operators. Zbl 0833.35032
Laptev, A.
1
1995
Eigenvalue bounds of mixed Steklov problems. Zbl 1442.35280
Hassannezhad, Asma; Laptev, Ari
1
2020
Inequalities involving Aharonov-Bohm magnetic potentials in dimensions \(2\) and \(3\). Zbl 07409790
Bonheure, Denis; Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
1
2021
Lieb-Thirring inequalities on the sphere. Zbl 1450.35195
Ilyin, A.; Laptev, A.
1
2020
On the Lieb-Thirring constant on the torus. Zbl 1436.35268
Zelik, S. V.; Ilyin, A. A.; Laptev, A. A.
1
2019
Spectral inequalities for a class of integral operators. Zbl 07139970
Laptev, A.; Velicu, A.
1
2019
Functional analysis and operator theory for quantum physics. The Pavel Exner anniversary volume. Dedicated to Pavel Exner on the occasion of his 70th birthday. Zbl 1364.46005
1
2017
Lieb-Thirring constant on the sphere and on the torus. Zbl 1450.35196
Ilyin, Alexei; Laptev, Ari; Zelik, Sergey
1
2020
Magnetic Lieb-Thirring inequality for periodic functions. Zbl 1453.35007
Ilyin, A. A.; Laptev, A. A.
1
2020
Spectral properties of the logarithmic Laplacian. Zbl 1476.35153
Laptev, Ari; Weth, Tobias
2
2021
Inequalities involving Aharonov-Bohm magnetic potentials in dimensions \(2\) and \(3\). Zbl 07409790
Bonheure, Denis; Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
1
2021
Symmetry results in two-dimensional inequalities for Aharonov-Bohm magnetic fields. Zbl 1439.81049
Bonheure, Denis; Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
3
2020
On the improvement of the Hardy inequality due to singular magnetic fields. Zbl 1450.35011
Fanelli, Luca; Krejčiřík, David; Laptev, Ari; Vega, Luis
3
2020
Eigenvalue bounds of mixed Steklov problems. Zbl 1442.35280
Hassannezhad, Asma; Laptev, Ari
1
2020
Lieb-Thirring inequalities on the sphere. Zbl 1450.35195
Ilyin, A.; Laptev, A.
1
2020
Lieb-Thirring constant on the sphere and on the torus. Zbl 1450.35196
Ilyin, Alexei; Laptev, Ari; Zelik, Sergey
1
2020
Magnetic Lieb-Thirring inequality for periodic functions. Zbl 1453.35007
Ilyin, A. A.; Laptev, A. A.
1
2020
Hardy inequalities for Landau Hamiltonian and for Baouendi-Grushin operator with Aharonov-Bohm type magnetic field. I. Zbl 1428.26029
Laptev, Ari; Ruzhansky, Michael; Yessirkegenov, Nurgissa
2
2019
Eigenvalues of the bilayer graphene operator with a complex valued potential. Zbl 1429.81034
Safronov, Oleg; Laptev, Ari; Ferrulli, Francesco
2
2019
Weyl asymptotics for perturbed functional difference operators. Zbl 1427.81063
Laptev, Ari; Schimmer, Lukas; Takhtajan, Leon A.
2
2019
On the Lieb-Thirring constant on the torus. Zbl 1436.35268
Zelik, S. V.; Ilyin, A. A.; Laptev, A. A.
1
2019
Spectral inequalities for a class of integral operators. Zbl 07139970
Laptev, A.; Velicu, A.
1
2019
Trace formulae for Schrödinger operators with complex-valued potentials on cubic lattices. Zbl 1403.39017
Korotyaev, Evgeny; Laptev, Ari
8
2018
Magnetic rings. Zbl 1390.81142
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
5
2018
Interpolation inequalities and spectral estimates for magnetic operators. Zbl 1388.81104
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
3
2018
A bound for the eigenvalue counting function for Krein-von Neumann and Friedrichs extensions. Zbl 1362.35197
Ashbaugh, Mark S.; Gesztesy, Fritz; Laptev, Ari; Mitrea, Marius; Sukhtaiev, Selim
3
2017
Finding eigenvalues and eigenfunctions of the Zaremba problem for the circle. Zbl 1367.47052
Laptev, Ari; Peicheva, Anastasiya; Shlapunov, Alexander
3
2017
Trace formulas for a discrete Schrödinger operator. Zbl 06835370
Korotyaev, E. L.; Laptev, A.
2
2017
Perturbations of embedded eigenvalues for a magnetic Schrödinger operator on a cylinder. Zbl 1355.81085
Laptev, Ari; Maad Sasane, Sara
1
2017
Functional analysis and operator theory for quantum physics. The Pavel Exner anniversary volume. Dedicated to Pavel Exner on the occasion of his 70th birthday. Zbl 1364.46005
1
2017
On the number of eigenvalues of Schrödinger operators with complex potentials. Zbl 1358.35074
Frank, Rupert L.; Laptev, Ari; Safronov, Oleg
24
2016
Weyl type asymptotics and bounds for the eigenvalues of functional-difference operators for mirror curves. Zbl 1361.47004
Laptev, Ari; Schimmer, Lukas; Takhtajan, Leon A.
19
2016
One-dimensional interpolation inequalities, Carlson-Landau inequalities, and magnetic Schrödinger operators. Zbl 1336.35016
Ilyin, Alexei; Laptev, Ari; Loss, Michael; Zelik, Sergey
8
2016
Lieb-Thirring inequalities on the torus. Zbl 1365.35096
Ilyin, Alexei A.; Laptev, Ari A.
4
2016
On continuous and discrete Hardy inequalities. Zbl 1368.35010
Kapitanski, Lev; Laptev, Ari
2
2016
Hardy inequalities with homogeneous weights. Zbl 1322.35103
Hoffmann-Ostenhof, Thomas; Laptev, Ari
10
2015
Hardy inequalities for \(p\)-Laplacians with Robin boundary conditions. Zbl 1360.47008
Ekholm, Tomas; Kovařík, Hynek; Laptev, Ari
5
2015
A bound for the eigenvalue counting function for higher-order Krein Laplacians on open sets. Zbl 1339.35202
Gesztesy, F.; Mitrea, M.; Sukhtaiev, S.; Laptev, A.
1
2015
One-dimensional Gagliardo-Nirenberg-Sobolev inequalities: remarks on duality and flows. Zbl 1320.26017
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
23
2014
Eigenvalue estimates for non-selfadjoint Dirac operators on the real line. Zbl 1287.81050
Cuenin, Jean-Claude; Laptev, Ari; Tretter, Christiane
22
2014
Spectral estimates on the sphere. Zbl 1293.35183
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari
16
2014
On some sharp spectral inequalities for Schrödinger operators on semiaxis. Zbl 1297.35155
Exner, Pavel; Laptev, Ari; Usman, Muhammad
5
2014
Spectral properties of Schrödinger operators on compact manifolds: rigidity, flows, interpolation and spectral estimates. Zbl 1276.58007
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
10
2013
On spectral estimates for two-dimensional Schrödinger operators. Zbl 1294.35048
Laptev, Ari; Solomyak, Michael
9
2013
Operator methods in mathematical physics. Conference on operator theory, analysis and mathematical physics (OTAMP) 2010, Bedlewo, Poland. Zbl 1257.00017
1
2013
Hardy inequalities for Robin Laplacians. Zbl 1242.26022
Kovařík, Hynek; Laptev, Ari
10
2012
On the negative spectrum of the two-dimensional Schrödinger operator with radial potential. Zbl 1253.35037
Laptev, A.; Solomyak, M.
10
2012
Hardy inequalities for a magnetic Grushin operator with Aharonov-Bohm type magnetic field. Zbl 1238.35014
Aermark, L.; Laptev, Ari
6
2012
Spectral inequalities for partial differential equations and their applications. Zbl 1269.35050
Laptev, Ari
3
2012
Geometrical versions of improved Berezin-Li-Yau inequalities. Zbl 1257.35138
Geisinger, Leander; Laptev, Ari; Weidl, Timo
16
2011
A sharp bound on eigenvalues of Schrödinger operators on the half-line with complex-valued potentials. Zbl 1253.35086
Frank, Rupert L.; Laptev, Ari; Seiringer, Robert
15
2011
Hardy inequalities for nonconvex domains. Zbl 1183.26017
Avkhadiev, Farit; Laptev, Ari
21
2010
Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. Zbl 1198.35161
Frank, Rupert L.; Laptev, Ari
4
2010
Around the research of Vladimir Maz’ya. II. Partial differential equations. Zbl 1180.47002
1
2010
Mikhail Shlemovich Birman (obituary). Zbl 1219.01025
Babich, V. M.; Buslaev, V. S.; Vershik, A. M.; Gindikin, S. G.; Kislyakov, S. V.; Laptev, A.; Marchenko, V. A.; Nikol’skii, N. K.; Pastur, L. A.; Plamenevskii, B. A.; Solomyak, M. Z.; Suslina, T. A.; Ural’tseva, N. N.; Faddeev, L. D.; Khavin, V. P.; Yafaev, D. R.
1
2010
Eigenvalue estimates for Schrödinger operators with complex potentials. Zbl 1185.35045
Laptev, Ari; Safronov, Oleg
50
2009
Lieb-Thirring inequalities with improved constants. Zbl 1152.35451
Dolbeault, Jean; Laptev, Ari; Loss, Michael
33
2008
Many-particle Hardy inequalities. Zbl 1135.35012
Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Laptev, A.; Tidblom, J.
15
2008
Hardy inequalities for simply connected planar domains. Zbl 1168.26003
Laptev, Ari; Sobolev, Alexander V.
8
2008
Spectral inequalities for Schrödinger operators with surface potentials. Zbl 1170.35486
Frank, Rupert L.; Laptev, Ari
6
2008
Eigenvalue estimates for magnetic Schrödinger operators in domains. Zbl 1186.35119
Frank, Rupert L.; Laptev, Ari; Molchanov, Stanislav
5
2008
Sharp spectral inequalities for the Heisenberg Laplacian. Zbl 1157.58008
Hansson, A. M.; Laptev, Ari
5
2008
Inverse spectral problems for Schrödinger operators with energy depending potentials. Zbl 1146.35095
Laptev, A.; Shterenberg, R.; Sukhanov, V.
2
2007
Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382
Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert
44
2006
Solitons and the removal of eigenvalues for fourth-order differential operators. Zbl 1123.34067
Hoppe, J.; Laptev, A.; Östensson, J.
6
2006
Reflectionless potentials for an ordinary differential operator of order four. Zbl 1103.34071
Laptev, A.; Shterenberg, R.; Sukhanov, V.; Östensson, J.
2
2006
Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials. Zbl 1077.81040
Laptev, A.; Naboko, S.; Safronov, O.
23
2005
A Szegő condition for a multidimensional Schrödinger operator. Zbl 1135.35355
Laptev, A.; Naboko, S.; Safronov, O.
7
2005
The negative discrete spectrum of a class of two-dimensional Schrödinger operators with magnetic fields. Zbl 1083.35070
Laptev, A.; Safronov, O.
2
2005
Generalized Hardy inequality for the magnetic Dirichlet forms. Zbl 1127.26015
Balinsky, Alexander; Laptev, Ari; Sobolev, Alexander V.
17
2004
Nonlinear eigenvalues and analytic hypoellipticity. Zbl 1053.35045
Chanillo, Sagun; Helffer, Bernard; Laptev, Ari
12
2004
On new relations between spectral properties of Jacobi matrices and their coefficients. Zbl 1135.47303
Laptev, A.; Naboko, S.; Safronov, O.
25
2003
A geometrical version of Hardy’s inequality. Zbl 1012.26011
Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Laptev, A.
50
2002
Bound state asymptotics for elliptic operators with strongly degenerated symbols. Zbl 1045.35049
Laptev, Ari; Safronov, Oleg; Weidl, Timo
7
2002
Discrete spectrum of a two-dimensional periodic elliptic second order operator perturbed by a decaying potential. I: Semibounded gap. Zbl 1070.47041
Birman, M. Sh.; Laptev, A.; Suslina, T. A.
2
2001
Sharp Lieb-Thirring inequalities in high dimensions. Zbl 1142.35531
Laptev, Ari; Weidl, Timo
72
2000
Recent results on Lieb-Thirring inequalities. Zbl 1135.81337
Laptev, Ari; Weidl, Timo
44
2000
New bounds on the Lieb-Thirring constants. Zbl 1074.35569
Hundertmark, D.; Laptev, A.; Weidl, T.
25
2000
Global Fourier integral operators and semiclassical asymptotics. Zbl 0962.35201
Laptev, A.; Sigal, I. M.
14
2000
The negative spectrum of a class of two-dimensional Schrödinger operators with potentials depending only on radius. Zbl 0972.35079
Laptev, A.
4
2000
Hardy inequalities for magnetic Dirichlet forms. Zbl 0977.26005
Laptev, Ari; Weidl, Timo
61
1999
On the negative eigenvalues of a class of Schrödinger operators. Zbl 0941.35055
Laptev, A.; Netrusov, Yu.
7
1999
On the Lieb-Thirring conjecture for a class of potentials. Zbl 0938.35112
Laptev, Ari
5
1999
On the eigenvalue behaviour for a class of differential operators on the semiaxis. Zbl 0916.34067
Birman, M. Sh.; Laptev, A.; Solomyak, M.
9
1998
Remarks on the paper of V. Guillemin and K. Okikiolu: “Subprincipal terms in Szegő estimates”. Zbl 0917.58046
Laptev, A.; Robert, D.; Safarov, Yu.
3
1998
Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces. Zbl 0892.35115
Laptev, A.
60
1997
The negative discrete spectrum of the operator \((-\Delta)^ l-\alpha V\) in \(L_ 2(\mathbb{R}^ d)\) for \(d\) even and \(2l\geq d\). Zbl 0876.35079
Birman, Mikhail Sh.; Laptev, Ari; Solomyak, Michael
9
1997
“Non-standard” spectral asymptotics for a two-dimensional Schrödinger operator. Zbl 0910.35086
Birman, Mikhail Sh.; Laptev, Ari
1
1997
The negative discrete spectrum of a two-dimensional Schrödinger operator. Zbl 0864.35080
Birman, M. Sh.; Laptev, A.
26
1996
Szegö type limit theorems. Zbl 0878.47020
Laptev, A.; Safarov, Yu.
17
1996
A generalization of the Berezin-Lieb inequality. Zbl 0868.47016
Laptev, A.; Safarov, Yu.
6
1996
On inequalities for the bound states of Schrödinger operators. Zbl 0833.35032
Laptev, A.
1
1995
Discrete spectrum of the perturbed Dirac operator. Zbl 0822.35104
Birman, Mikhail Sh.; Laptev, Ari
13
1994
On global representations of Lagrangian distributions and solutions of hyperbolic equations. Zbl 0811.35177
Laptev, A.; Safarov, Yu.; Vassiliev, D.
8
1994
Discrete spectrum of the perturbed Dirac operator. Zbl 0858.47004
Birman, M. Sh.; Laptev, A.
4
1994
Asymptotics of the negative discrete spectrum of a class of Schrödinger operators with large coupling constant. Zbl 0795.35071
Laptev, Ari
3
1993
Error estimate in the generalized Szegö theorem. Zbl 0743.58032
Laptev, A.; Safarov, Yu.
1
1991
Spectral asymptotics of a class of Fourier integral operators. Zbl 0535.47030
Laptev, A. A.
2
1983
Spectral asymptotics of a certain class of Fourier integral operators. Zbl 0503.47044
Laptev, A. A.
5
1981
On estimates of singular numbers for a class of integral operators. Zbl 0478.47032
Laptev, A. A.
2
1981
On an estimate of the remainder term in formulas of the spectral asymptotics for one class of integral operators. Zbl 0443.47051
Laptev, A. A.
4
1977
Spectral asymptotics of a composition of pseudodifferential operators and reflections from the boundary. Zbl 0391.47035
Laptev, A. A.
1
1977
Spectral asymptotic behavior of a class of integral operators. Zbl 0322.45003
Laptev, A. A.
2
1975
all top 5

Cited by 625 Authors

52 Laptev, Ari
25 Frank, Rupert L.
20 Avkhadiev, Farit Gabidinovich
20 Safronov, Oleg
19 Dolbeault, Jean
15 Ilyin, Alexei A.
15 Kovařík, Hynek
15 Nasibullin, Ramil Gaisa’evich
14 Korotyaev, Evgeny L.
14 Loss, Michael
12 Cuenin, Jean-Claude
12 Esteban, Maria J.
12 Krejčiřík, David
12 Simon, Barry
11 Fanelli, Luca
10 Felli, Veronica
10 Solomyak, Mikhaĭl Zakharovich
9 Abatangelo, Laura
9 Weidl, Timo
8 Ruzhansky, Michael V.
8 Seiringer, Robert
8 Yolcu, Selma Yıldırım
8 Zelik, Sergey V.
7 Gesztesy, Fritz
7 Hansmann, Marcel
7 Larson, Simon
7 Mariño, Marcos
7 Tertikas, Achilles
7 Yolcu, Turkay
6 Ekholm, Tomas
6 Filippas, Stathis
6 Grassi, Alba
6 Harrell, Evans M. II
6 Lundholm, Douglas
6 Rozenblum, Grigori V.
6 Suragan, Durvudkhan
5 Birman, Mikhail Shlëmovich
5 Chen, Hua
5 Denisov, Sergey A.
5 Lukic, Milivoje
5 Phan Thành Nam
5 Pushnitski, Alexander B.
5 Schimmer, Lukas
4 Barbatis, Gerassimos
4 Barseghyan, Diana
4 Bove, Antonio
4 Cossetti, Lucrezia
4 Evans, William Desmond
4 Exner, Pavel
4 Helffer, Bernard
4 Hundertmark, Dirk
4 Ibrogimov, Orif O.
4 Kachmar, Ayman
4 Karuhanga, Martin
4 Lam, Nguyen
4 Laugesen, Richard Snyder
4 Léna, Corentin
4 Lewin, Mathieu
4 Lewis, Roger T.
4 Lieb, Elliott Hershel
4 Makarov, R. V.
4 Malamud, Mark M.
4 Molchanov, Stanislav Alekseevich
4 Naboko, Serguei N.
4 Rădulescu, Vicenţiu D.
4 Rohleder, Jonathan
4 Shafigullin, Il’nar Kasyĭmovich
4 Siegl, Petr
4 Solovej, Jan Philip
4 Stubbe, Joachim
4 Takhtajan, Leon Armenovich
4 Vega, Luis
4 Zanelli, Lorenzo
3 Behrndt, Jussi
3 Cassano, Biagio
3 Damanik, David
3 Demuth, Michael
3 Dostanić, Milutin R.
3 Gao, Xiaofen
3 Geisinger, Leander
3 Gontier, David
3 Grubb, Gerd
3 Gu, Jie
3 Hainzl, Christian
3 Hermi, Lotfi
3 Himonas, A. Alexandrou
3 Hoffmann-Ostenhof, Thomas
3 Hulko, Artem
3 Lotoreichik, Vladimir
3 Lu, Guozhen
3 Melnikov, Yuri B.
3 Mughetti, Marco
3 Neidhardt, Hagen
3 Nys, Manon
3 Petronilho, Gerson
3 Portmann, Fabian
3 Robert, Didier
3 Safarov, Yuri G.
3 Sambou, Diomba
3 Shargorodsky, Eugene
...and 525 more Authors
all top 5

Cited in 151 Serials

54 Journal of Functional Analysis
36 Communications in Mathematical Physics
33 Journal of Mathematical Analysis and Applications
33 Journal of Mathematical Physics
23 Journal of Spectral Theory
18 Calculus of Variations and Partial Differential Equations
16 Journal of Differential Equations
15 Letters in Mathematical Physics
15 St. Petersburg Mathematical Journal
15 Annales Henri Poincaré
14 Advances in Mathematics
12 Proceedings of the American Mathematical Society
11 Integral Equations and Operator Theory
10 Bulletin of Mathematical Sciences
9 Reviews in Mathematical Physics
9 Journal of Mathematical Sciences (New York)
8 Functional Analysis and its Applications
8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
7 Transactions of the American Mathematical Society
7 Communications in Partial Differential Equations
7 Journal de Mathématiques Pures et Appliquées. Neuvième Série
7 Potential Analysis
7 Lobachevskii Journal of Mathematics
6 Arkiv för Matematik
6 Duke Mathematical Journal
6 Discrete and Continuous Dynamical Systems
6 Mathematical Physics, Analysis and Geometry
6 Journal of the European Mathematical Society (JEMS)
6 Communications in Contemporary Mathematics
6 Analysis and Mathematical Physics
5 Annales de l’Institut Fourier
5 Mathematische Nachrichten
5 The Journal of Geometric Analysis
5 Russian Mathematics
5 Doklady Mathematics
5 Journal of High Energy Physics
5 Ufimskiĭ Matematicheskiĭ Zhurnal
4 Reports on Mathematical Physics
4 Russian Journal of Mathematical Physics
4 Journal of Physics A: Mathematical and Theoretical
3 Applicable Analysis
3 Archive for Rational Mechanics and Analysis
3 Journal d’Analyse Mathématique
3 Nonlinearity
3 Russian Mathematical Surveys
3 ZAMP. Zeitschrift für angewandte Mathematik und Physik
3 Archiv der Mathematik
3 Inventiones Mathematicae
3 Journal of Approximation Theory
3 Acta Applicandae Mathematicae
3 Journal of Scientific Computing
3 SIAM Journal on Mathematical Analysis
3 Sbornik: Mathematics
3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
3 Journal of Inequalities and Applications
3 Advanced Nonlinear Studies
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
3 Communications on Pure and Applied Analysis
3 Complex Analysis and Operator Theory
2 Journal of Statistical Physics
2 Mathematical Notes
2 Czechoslovak Mathematical Journal
2 Journal of Computational and Applied Mathematics
2 Journal of Soviet Mathematics
2 Mathematica Scandinavica
2 Siberian Mathematical Journal
2 Chinese Annals of Mathematics. Series B
2 Constructive Approximation
2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
2 NoDEA. Nonlinear Differential Equations and Applications
2 Bulletin des Sciences Mathématiques
2 The Journal of Fourier Analysis and Applications
2 Revista Matemática Complutense
2 Milan Journal of Mathematics
2 Mediterranean Journal of Mathematics
2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
2 Journal of Fixed Point Theory and Applications
2 Banach Journal of Mathematical Analysis
1 Classical and Quantum Gravity
1 Communications on Pure and Applied Mathematics
1 Indian Journal of Pure & Applied Mathematics
1 Israel Journal of Mathematics
1 Journal of Mathematical Biology
1 Mathematics of Computation
1 Acta Mathematica
1 Canadian Journal of Mathematics
1 Collectanea Mathematica
1 Geometriae Dedicata
1 Illinois Journal of Mathematics
1 Publications Mathématiques
1 Journal of the London Mathematical Society. Second Series
1 Journal of the Mathematical Society of Japan
1 Journal für die Reine und Angewandte Mathematik
1 Le Matematiche
1 Mathematische Annalen
1 Mathematische Zeitschrift
1 Memoirs of the American Mathematical Society
1 Monatshefte für Mathematik
1 Numerische Mathematik
1 Publications of the Research Institute for Mathematical Sciences, Kyoto University
...and 51 more Serials
all top 5

Cited in 46 Fields

405 Partial differential equations (35-XX)
206 Operator theory (47-XX)
195 Quantum theory (81-XX)
91 Real functions (26-XX)
66 Ordinary differential equations (34-XX)
55 Functional analysis (46-XX)
51 Global analysis, analysis on manifolds (58-XX)
28 Difference and functional equations (39-XX)
23 Harmonic analysis on Euclidean spaces (42-XX)
23 Statistical mechanics, structure of matter (82-XX)
21 Calculus of variations and optimal control; optimization (49-XX)
15 Special functions (33-XX)
13 Dynamical systems and ergodic theory (37-XX)
12 Differential geometry (53-XX)
12 Optics, electromagnetic theory (78-XX)
11 Numerical analysis (65-XX)
10 Algebraic geometry (14-XX)
10 Probability theory and stochastic processes (60-XX)
10 Fluid mechanics (76-XX)
10 Relativity and gravitational theory (83-XX)
9 Functions of a complex variable (30-XX)
7 Combinatorics (05-XX)
6 Mechanics of deformable solids (74-XX)
5 History and biography (01-XX)
5 Topological groups, Lie groups (22-XX)
5 Potential theory (31-XX)
5 Integral equations (45-XX)
4 Abstract harmonic analysis (43-XX)
4 Integral transforms, operational calculus (44-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
3 Statistics (62-XX)
3 Mechanics of particles and systems (70-XX)
2 Group theory and generalizations (20-XX)
2 Measure and integration (28-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Approximations and expansions (41-XX)
2 Biology and other natural sciences (92-XX)
2 Information and communication theory, circuits (94-XX)
1 General and overarching topics; collections (00-XX)
1 Number theory (11-XX)
1 \(K\)-theory (19-XX)
1 Convex and discrete geometry (52-XX)
1 Manifolds and cell complexes (57-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Astronomy and astrophysics (85-XX)
1 Systems theory; control (93-XX)

Citations by Year

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