Edit Profile (opens in new tab) Borisov, Denis Ivanovich Co-Author Distance Author ID: borisov.denis-i Published as: Borisov, D. I.; Borisov, Denis; Borisov, Denis I.; Borisov, D.; Borisov, Denis Ivanovich more...less Homepage: http://borisovdi.narod.ru/ External Links: MGP · ORCID · Math-Net.Ru · dblp Documents Indexed: 143 Publications since 1999, including 10 Additional arXiv Preprints Reviewing Activity: 48 Reviews Co-Authors: 41 Co-Authors with 88 Joint Publications 1,050 Co-Co-Authors all top 5 Co-Authors 50 single-authored 14 Cardone, Giuseppe 11 Veselić, Ivan 7 Exner, Pavel 7 Freitas, Pedro 7 Gadyl’shin, Rustem R. 7 Mukhametrakhimova, Albina I. 7 Zezyulin, Dmitry A. 7 Znojil, Miloslav 5 Konyrkulzhaeva, Maral Nurlanovna 4 Bunoiu, Renata 4 Golovina, Anastasiya Mihajlovna 3 Dmitriev, Sergey V. 3 Krejčiřík, David 3 Pankrashkin, Konstantin 3 Piatnitski, Andrey L. 3 Tautenhahn, Martin 3 Zhizhina, Elena Anatol’evna 2 Durante, Tiziana 2 Hoecker-Escuti, Francisco 2 Kevrekidis, Panayotis G. 2 Saadatmand, Danial 2 Sharapov, Timur Farkhatovich 2 Täufer, Matthias 1 Berkolaiko, Gregory 1 Bikmetov, Aĭdar Renatovich 1 Chechkin, Gregory Aleksandrovich 1 Ekholm, Tomas 1 Faella, Luisa 1 Fatykhov, Minnekhan A. 1 Gaydukov, R. K. 1 Gazizova, L. I. 1 Golovina, Anastasia 1 Javidan, Kurosh 1 King, Marshall 1 Koroleva, Yulia O. 1 Kovařík, Hynek 1 Nakić, Ivica 1 Perugia, Carmen 1 Rose, Christian 1 Ružička, František 1 Sultanov, Oskar A. 1 Zhou, Kun all top 5 Serials 20 Journal of Mathematical Sciences (New York) 6 Journal of Mathematical Physics 6 Sbornik: Mathematics 6 Doklady Mathematics 5 Mathematical Notes 5 Theoretical and Mathematical Physics 5 Russian Journal of Mathematical Physics 5 Annales Henri Poincaré 5 Proceedings of the Steklov Institute of Mathematics 4 Journal of Differential Equations 4 Journal of Physics A: Mathematical and Theoretical 4 Ufimskiĭ Matematicheskiĭ Zhurnal 3 Journal of Mathematical Analysis and Applications 3 Journal of Functional Analysis 3 Annals of Physics 3 Izvestiya: Mathematics 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Statistical Physics 2 Functional Analysis and its Applications 2 Studies in Applied Mathematics 2 Asymptotic Analysis 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Communications in Nonlinear Science and Numerical Simulation 2 Communications in Contemporary Mathematics 2 Differential Equations 2 Analysis and Mathematical Physics 1 International Journal of Theoretical Physics 1 Nuclear Physics. B 1 Russian Mathematical Surveys 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Advances in Mathematics 1 Integral Equations and Operator Theory 1 Sibirskiĭ Matematicheskiĭ Zhurnal 1 Zeitschrift für Analysis und ihre Anwendungen 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Journal of Theoretical Probability 1 Applied Mathematics Letters 1 Journal of Physics A: Mathematical and General 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Communications in Analysis and Geometry 1 Calculus of Variations and Partial Differential Equations 1 St. Petersburg Mathematical Journal 1 Problemy Matematicheskogo Analiza 1 Mathematical Physics, Analysis and Geometry 1 Visnyk Kharkivs’kogo Universytetu. Seriya Matematyka, Prykladna Matematyka i Mekhanika 1 Analysis & PDE 1 Bulletin of Mathematical Sciences all top 5 Fields 95 Partial differential equations (35-XX) 45 Quantum theory (81-XX) 39 Operator theory (47-XX) 25 Ordinary differential equations (34-XX) 13 Statistical mechanics, structure of matter (82-XX) 6 Probability theory and stochastic processes (60-XX) 4 Combinatorics (05-XX) 4 Optics, electromagnetic theory (78-XX) 3 Algebraic geometry (14-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Approximations and expansions (41-XX) 2 Functional analysis (46-XX) 2 Fluid mechanics (76-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Differential geometry (53-XX) 1 Mechanics of deformable solids (74-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 105 Publications have been cited 832 times in 351 Documents Cited by ▼ Year ▼ Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve. Zbl 1361.35021 Borisov, Denis; Cardone, Giuseppe; Durante, Tiziana 34 2016 Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in \(\mathbb R^d\). Zbl 1180.35397 Borisov, Denis; Freitas, Pedro 32 2010 Bound states in weakly deformed strips and layers. Zbl 1043.35046 Borisov, D.; Exner, P.; Gadyl’shin, R.; Krejčiřík, D. 31 2001 Discrete spectrum of an asymmetric pair of waveguides coupled through a window. Zbl 1156.35066 Borisov, D. I. 31 2006 Homogenization of the planar waveguide with frequently alternating boundary conditions. Zbl 1178.81088 Borisov, D.; Cardone, G. 30 2009 Geometric coupling thresholds in a two-dimensional strip. Zbl 1060.35094 Borisov, D.; Exner, P.; Gadyl’shin, R. 29 2002 Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains. Zbl 1168.35401 Borisov, Denis; Freitas, Pedro 29 2009 Waveguide with non-periodically alternating Dirichlet and Robin conditions: Homogenization and asymptotics. Zbl 1282.35033 Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe 29 2013 \(\mathcal {PT}\)-symmetric waveguides. Zbl 1178.35141 Borisov, Denis; Krejčiřík, David 26 2008 On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition. Zbl 1210.82077 Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe 26 2010 Uniform resolvent convergence for strip with fast oscillating boundary. Zbl 1286.35025 Borisov, Denis; Cardone, Giuseppe; Faella, Luisa; Perugia, Carmen 24 2013 Exponential splitting of bound states in a waveguide with a pair of distant windows. Zbl 1050.81008 Borisov, D.; Exner, P. 20 2004 Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones. Zbl 1269.81050 Borisov, Denis; Pankrashkin, Konstantin 20 2013 Gap opening and split band edges in waveguides coupled by a periodic system of small windows. Zbl 1288.81046 Borisov, D. I.; Pankrashkin, K. V. 18 2013 On a model boundary value problem for Laplacian with frequently alternating type of boundary condition. Zbl 1137.35308 Borisov, Denis I. 17 2003 On the spectrum of a periodic operator with a small localized perturbation. Zbl 1169.34056 Borisov, D. I.; Gadyl’shin, R. R. 16 2008 Distant perturbations of the Laplacian in a multi-dimensional space. Zbl 1143.35075 Borisov, Denis I. 15 2007 Homogenization and asymptotics for a waveguide with an infinite number of closely located small windows. Zbl 1290.81038 Borisov, D.; Bunoiu, R.; Cardone, G. 14 2011 Asymptotic behaviour of the spectrum of a waveguide with distant perturbations. Zbl 1185.35155 Borisov, Denis 14 2007 Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation. Zbl 1181.35151 Borisov, Denis; Freitas, Pedro 13 2009 Asymptotics and estimates for the eigenelements of the Laplacian with frequent nonperiod change of boundary conditions. Zbl 1067.35055 Borisov, D. I. 12 2003 Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients. Zbl 1206.35029 Borisov, D. 12 2009 The norm resolvent convergence for elliptic operators in multi-dimensional domains with small holes. Zbl 1403.35023 Borisov, D. I.; Mukhametrakhimova, A. I. 11 2018 Spectrum of the magnetic Schrödinger operator in a waveguide with combined boundary conditions. Zbl 1077.81038 Borisov, Denis; Ekholm, Tomas; Kovařík, Hynek 11 2005 The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions. Zbl 1241.47042 Borisov, Denis; Krejčiřík, David 11 2012 Planar waveguide with ”twisted” boundary conditions: Discrete spectrum. Zbl 1273.81100 Borisov, Denis; Cardone, Giuseppe 10 2011 On a waveguide with an infinite number of small windows. (Sur un guide d’onde avec un nombre infini de petites fentes.) Zbl 1211.35098 Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe 10 2011 Distant perturbation asymptotics in window-coupled waveguides. I: The nonthreshold case. Zbl 1112.81043 Borisov, D.; Exner, P. 10 2006 Low lying eigenvalues of randomly curved quantum waveguides. Zbl 1292.81051 Borisov, Denis; Veselić, Ivan 9 2013 On the band spectrum of a Schrödinger operator in a periodic system of domains coupled by small windows. Zbl 1319.35134 Borisov, D. I. 9 2015 Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods. Zbl 1223.35248 Borisov, Denis; Cardone, Giuseppe 9 2011 On the spectrum of a two-dimensional periodic operator with a small localized perturbation. Zbl 1233.35066 Borisov, D. I. 9 2011 Low lying spectrum of weak-disorder quantum waveguides. Zbl 1208.82089 Borisov, Denis; Veselić, Ivan 9 2011 Scale-free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations. Zbl 1381.35027 Borisov, Denis; Tautenhahn, Martin; Veselić, Ivan 8 2017 Tunneling resonances in systems without a classical trapping. Zbl 1280.81035 Borisov, D.; Exner, P.; Golovina, A. 8 2013 The spectrum of two quantum layers coupled by a window. Zbl 1115.81024 Borisov, D. 8 2007 Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition. Zbl 1480.35140 Borisov, D. I.; Mukhametrakhimova, A. I. 7 2021 Some singular perturbations of periodic operators. Zbl 1147.34060 Borisov, D. I. 7 2007 On a \(\mathcal{PT}\)-symmetric waveguide with a pair of small holes. Zbl 1321.47166 Borisov, D. I. 6 2013 Planar waveguide with “twisted” boundary conditions: small width. Zbl 1274.81108 Borisov, Denis; Cardone, Giuseppe 6 2012 On the spectral stability of kinks in 2D Klein-Gordon model with parity-time-symmetric perturbation. Zbl 1364.35305 Borisov, D. I.; Dmitriev, S. V. 6 2017 The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential. Zbl 1177.34107 Borisov, D. I.; Gadyl’shin, R. R. 6 2006 Boundary-value problem in a cylinder with frequently changing type of boundary conditions. Zbl 1045.35047 Borisov, D. I. 6 2002 Two patterns of \(\mathcal{PT}\)-symmetry breakdown in a non-numerical six-state simulation. Zbl 1390.81172 Znojil, Miloslav; Borisov, Denis I. 5 2018 Existence of the stationary solution of a Rayleigh-type equation. Zbl 1408.35118 Borisov, D. I.; Gaydukov, R. K. 5 2016 Multiply degenerate exceptional points and quantum phase transitions. Zbl 1329.81037 Borisov, Denis I.; Ružička, František; Znojil, Miloslav 5 2015 On the spectrum of the Laplacian with frequently alternating boundary conditions. Zbl 0945.35066 Borisov, D. I.; Gadyl’shin, R. R. 5 1999 On eigenvalues of a \(\mathcal{PT}\)-symmetric operator in a thin layer. Zbl 1371.35178 Borisov, Denis I.; Znojil, Miloslav 5 2017 Perturbation of threshold of the essential spectrum of the Schrödinger operator on the simplest graph with a small edge. Zbl 1426.34039 Borisov, D. I.; Konyrkulzhaeva, M. N. 5 2019 Asymptotics for the expected lifetime of Brownian motion on thin domains in \(\mathbb R^n\). Zbl 1296.60220 Borisov, Denis; Freitas, Pedro 5 2013 On the extrema of band functions in periodic waveguides. Zbl 1308.34111 Borisov, D. I.; Pankrashkin, K. V. 5 2013 Two-parameter asymptotics in a boundary value problem for the Laplacian. Zbl 1140.35544 Borisov, D. I. 5 2001 Kink scattering from a parity-time-symmetric defect in the \(\phi^4\) model. Zbl 1510.35186 Saadatmand, Danial; Dmitriev, Sergey V.; Borisov, Denis I.; Kevrekidis, Panayotis G.; Fatykhov, Minnekhan A.; Javidan, Kurosh 5 2015 On a model graph with a loop and small edges. Holomorphy property of resolvent. Zbl 1458.34059 Borisov, D. I.; Mukhametrakhimova, A. I. 5 2020 The spectrum of geodesic balls on spherically symmetric manifolds. Zbl 1380.53047 Borisov, Denis; Freitas, Pedro 4 2017 Asymptotics and estimates of the convergence rate in a three-dimensional boundary value problem with rapidly alternating boundary conditions. Zbl 1108.35032 Borisov, D. I. 4 2004 Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials. Zbl 1427.81028 Borisov, D. I.; Zezyulin, D. A. 4 2020 Analyticity of resolvents of elliptic operators on quantum graphs with small edges. Zbl 1485.81032 Borisov, D. I. 4 2022 Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: vanishing limit. Zbl 1505.35025 Borisov, D. I.; Kříž, J. 4 2023 On the resolvent of multidimensional operators with frequently alternating boundary conditions with the Robin homogenized condition. Zbl 1346.35054 Borisov, D. I.; Sharapov, T. F. 4 2016 The spectrum of a self-adjoint differential operator with rapidly oscillating coefficients on the axis. Zbl 1137.34039 Borisov, D. I.; Gadyl’shin, R. R. 4 2007 Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations. Zbl 1468.35050 Borisov, D. I.; Zezyulin, D. A.; Znojil, M. 4 2021 Quantum Hamiltonians with weak random abstract perturbation. I: Initial length scale estimate. Zbl 1348.82039 Borisov, Denis; Golovina, Anastasia; Veselić, Ivan 3 2016 Absence of gaps in a lower part of the spectrum of a Laplacian with frequent alternation of boundary conditions in a strip. Zbl 1405.35020 Borisov, D. I. 3 2018 Norm-resolvent convergence for elliptic operators in domain with perforation along curve. Zbl 1304.35058 Borisov, Denis; Cardone, Giuseppe; Durante, Tiziana 3 2014 Expansion of the spectrum in the weak disorder regime for random operators in continuum space. Zbl 1386.35291 Borisov, Denis; Hoecker-Escuti, Francisco; Veselić, Ivan 3 2018 Norm resolvent convergence of elliptic operators in domains with thin spikes. Zbl 1486.35021 Borisov, D. I. 3 2022 On the spectrum of a non-self-adjoint quasiperiodic operator. Zbl 1506.47038 Borisov, D. I.; Fedotov, A. A. 3 2021 Gaps in the spectrum of the Laplacian in a strip with periodic delta interaction. Zbl 1430.35169 Borisov, D. I. 3 2019 On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets. Zbl 1210.34071 Borisov, D. I. 3 2006 Resonant interaction of \(\phi^4\) kink with \(\mathcal{PT}\)-symmetric perturbation with spatially periodic gain/loss coefficient. Zbl 1510.35185 Saadatmand, Danial; Borisov, Denis I.; Kevrekidis, Panayotis G.; Zhou, Kun; Dmitriev, Sergey V. 3 2018 Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum. Zbl 1463.34127 Borisov, Denis Ivanovich; Konyrkulzhaeva, Maral Nurlanovna 3 2019 Expansion of the almost sure spectrum in the weak disorder regime. Zbl 1331.82026 Borisov, Denis; Hoecker-Escuti, Francisco; Veselić, Ivan 2 2016 Creation of spectral bands for a periodic domain with small windows. Zbl 1342.81143 Borisov, D. I. 2 2016 On a Laplacian with frequently nonperiodically alternating boundary conditions. Zbl 1197.35027 Borisov, D. I. 2 2002 On the spectrum of deformations of compact double-sided flat hypersurfaces. Zbl 1282.35261 Borisov, Denis; Freitas, Pedro 2 2013 Multiscale unique continuation properties of eigenfunctions. Zbl 1337.35031 Borisov, Denis; Nakić, Ivica; Rose, Christian; Tautenhahn, Martin; Veselić, Ivan 2 2015 On a singularly perturbed boundary value problem for the Laplacian in a cylinder. Zbl 1274.35013 Borisov, D. I. 2 2002 Quantum graphs with small edges: holomorphy of resolvents. Zbl 1479.81026 Borisov, D. I. 2 2021 Operator estimates for planar domains with irregularly curved boundary. The Dirichlet and Neumann conditions. Zbl 1495.35017 Borisov, D. I. 2 2022 Bifurcations of essential spectra generated by a small non-Hermitian hole. II: Eigenvalues and resonances. Zbl 1498.35214 Borisov, D. I.; Zezyulin, D. A. 2 2022 Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators. Zbl 1339.81037 Borisov, D.; Tautenhahn, M.; Veselić, I. 2 2015 On the spectrum of the Schrödinger operator perturbed by a rapidly oscillating potential. Zbl 1134.34337 Borisov, D. I. 2 2006 Asymptotic analysis of mean exit time for dynamical systems with a single well potential. Zbl 1441.35020 Borisov, D.; Sultanov, O. 2 2020 On Bloch solutions of difference Schrödinger equations. Zbl 1512.39001 Borisov, D. I.; Fedotov, A. A. 2 2022 Bifurcations of essential spectra generated by a small non-Hermitian hole. I: Meromorphic continuations. Zbl 1479.35582 Borisov, D. I.; Zezyulin, D. A. 2 2021 On discrete spectrum of a model graph with loop and small edges. Zbl 1472.81069 Borisov, D. I.; Konyrkulzhaeva, M. N.; Mukhametrakhimova, A. I. 2 2021 Approximation of point interactions by geometric perturbations in two-dimensional domains. Zbl 1522.35029 Borisov, D. I.; Exner, P. 2 2023 Spectral localization for quantum Hamiltonians with weak random delta interaction. (Localisation spectrale pour des hamiltoniens quantiques, avec une faible interaction aléatoire delta.) Zbl 1401.35218 Borisov, Denis I.; Täufer, Matthias; Veselić, Ivan 1 2018 Perturbation of threshold of essential spectrum for waveguides with windows. II: Asymptotics. Zbl 1335.35162 Borisov, D. I. 1 2015 Bethe-Sommerfeld conjecture for periodic Schrödinger operators in strip. Zbl 1432.35062 Borisov, D. I. 1 2019 Mathematical and physical meaning of the crossings of energy levels in \(\mathcal {PT}\)-symmetric systems. Zbl 1402.81149 Borisov, Denis I.; Znojil, Miloslav 1 2016 Perturbation of threshold of essential spectrum for waveguides with windows. I: Decreasing resonance solutions. Zbl 1325.35119 Borisov, D. I. 1 2015 Discrete spectrum of the Schrödinger operator perturbed by a narrowly supported potential. Zbl 1178.35144 Bikmetov, A. R.; Borisov, D. I. 1 2005 Estimates of initial scales for layers with small random negative-definite perturbations. Zbl 1440.60058 Borisov, D. I. 1 2019 Operator \(L_2\)-estimates for two-dimensional problems with rapidly alternating boundary conditions. Zbl 1501.35154 Borisov, D. I.; Konyrkulzhaeva, M. N. 1 2022 Taylor series for resolvents of operators on graphs with small edges. Zbl 1505.35343 Borisov, D. I.; Gazizova, L. I. 1 2022 Spacing gain and absorption in a simple \(\mathcal{PT}\)-symmetric model: spectral singularities and ladders of eigenvalues and resonances. Zbl 1509.81525 Borisov, D. I.; Zezyulin, D. A. 1 2019 Anomalous mechanisms of the loss of observability in non-Hermitian quantum models. Zbl 1473.81151 Znojil, Miloslav; Borisov, Denis I. 1 2020 On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders. Zbl 1458.81018 Borisov, D. I.; Golovina, A. M. 1 2021 Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: vanishing limit. Zbl 1505.35025 Borisov, D. I.; Kříž, J. 4 2023 Approximation of point interactions by geometric perturbations in two-dimensional domains. Zbl 1522.35029 Borisov, D. I.; Exner, P. 2 2023 Analyticity of resolvents of elliptic operators on quantum graphs with small edges. Zbl 1485.81032 Borisov, D. I. 4 2022 Norm resolvent convergence of elliptic operators in domains with thin spikes. Zbl 1486.35021 Borisov, D. I. 3 2022 Operator estimates for planar domains with irregularly curved boundary. The Dirichlet and Neumann conditions. Zbl 1495.35017 Borisov, D. I. 2 2022 Bifurcations of essential spectra generated by a small non-Hermitian hole. II: Eigenvalues and resonances. Zbl 1498.35214 Borisov, D. I.; Zezyulin, D. A. 2 2022 On Bloch solutions of difference Schrödinger equations. Zbl 1512.39001 Borisov, D. I.; Fedotov, A. A. 2 2022 Operator \(L_2\)-estimates for two-dimensional problems with rapidly alternating boundary conditions. Zbl 1501.35154 Borisov, D. I.; Konyrkulzhaeva, M. N. 1 2022 Taylor series for resolvents of operators on graphs with small edges. Zbl 1505.35343 Borisov, D. I.; Gazizova, L. I. 1 2022 Asymptotics for problems in perforated domains with Robin nonlinear condition on the boundaries of cavities. Zbl 1522.35036 Borisov, Denis I.; Mukhametrakhimova, Albina I. 1 2022 Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition. Zbl 1480.35140 Borisov, D. I.; Mukhametrakhimova, A. I. 7 2021 Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations. Zbl 1468.35050 Borisov, D. I.; Zezyulin, D. A.; Znojil, M. 4 2021 On the spectrum of a non-self-adjoint quasiperiodic operator. Zbl 1506.47038 Borisov, D. I.; Fedotov, A. A. 3 2021 Quantum graphs with small edges: holomorphy of resolvents. Zbl 1479.81026 Borisov, D. I. 2 2021 Bifurcations of essential spectra generated by a small non-Hermitian hole. I: Meromorphic continuations. Zbl 1479.35582 Borisov, D. I.; Zezyulin, D. A. 2 2021 On discrete spectrum of a model graph with loop and small edges. Zbl 1472.81069 Borisov, D. I.; Konyrkulzhaeva, M. N.; Mukhametrakhimova, A. I. 2 2021 On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders. Zbl 1458.81018 Borisov, D. I.; Golovina, A. M. 1 2021 On elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary. Zbl 1458.35028 Borisov, D. I.; Cardone, Giuseppe; Chechkin, G. A.; Koroleva, Yu. O. 1 2021 On a model graph with a loop and small edges. Holomorphy property of resolvent. Zbl 1458.34059 Borisov, D. I.; Mukhametrakhimova, A. I. 5 2020 Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials. Zbl 1427.81028 Borisov, D. I.; Zezyulin, D. A. 4 2020 Asymptotic analysis of mean exit time for dynamical systems with a single well potential. Zbl 1441.35020 Borisov, D.; Sultanov, O. 2 2020 Anomalous mechanisms of the loss of observability in non-Hermitian quantum models. Zbl 1473.81151 Znojil, Miloslav; Borisov, Denis I. 1 2020 Analytic continuation of resolvents of elliptic operators in a multidimensional cylinder. Zbl 07251966 Borisov, D. I.; Golovina, A. M.; Mukhametrakhimova, A. I. 1 2020 Perturbation of threshold of the essential spectrum of the Schrödinger operator on the simplest graph with a small edge. Zbl 1426.34039 Borisov, D. I.; Konyrkulzhaeva, M. N. 5 2019 Gaps in the spectrum of the Laplacian in a strip with periodic delta interaction. Zbl 1430.35169 Borisov, D. I. 3 2019 Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum. Zbl 1463.34127 Borisov, Denis Ivanovich; Konyrkulzhaeva, Maral Nurlanovna 3 2019 Bethe-Sommerfeld conjecture for periodic Schrödinger operators in strip. Zbl 1432.35062 Borisov, D. I. 1 2019 Estimates of initial scales for layers with small random negative-definite perturbations. Zbl 1440.60058 Borisov, D. I. 1 2019 Spacing gain and absorption in a simple \(\mathcal{PT}\)-symmetric model: spectral singularities and ladders of eigenvalues and resonances. Zbl 1509.81525 Borisov, D. I.; Zezyulin, D. A. 1 2019 The norm resolvent convergence for elliptic operators in multi-dimensional domains with small holes. Zbl 1403.35023 Borisov, D. I.; Mukhametrakhimova, A. I. 11 2018 Two patterns of \(\mathcal{PT}\)-symmetry breakdown in a non-numerical six-state simulation. Zbl 1390.81172 Znojil, Miloslav; Borisov, Denis I. 5 2018 Absence of gaps in a lower part of the spectrum of a Laplacian with frequent alternation of boundary conditions in a strip. Zbl 1405.35020 Borisov, D. I. 3 2018 Expansion of the spectrum in the weak disorder regime for random operators in continuum space. Zbl 1386.35291 Borisov, Denis; Hoecker-Escuti, Francisco; Veselić, Ivan 3 2018 Resonant interaction of \(\phi^4\) kink with \(\mathcal{PT}\)-symmetric perturbation with spatially periodic gain/loss coefficient. Zbl 1510.35185 Saadatmand, Danial; Borisov, Denis I.; Kevrekidis, Panayotis G.; Zhou, Kun; Dmitriev, Sergey V. 3 2018 Spectral localization for quantum Hamiltonians with weak random delta interaction. (Localisation spectrale pour des hamiltoniens quantiques, avec une faible interaction aléatoire delta.) Zbl 1401.35218 Borisov, Denis I.; Täufer, Matthias; Veselić, Ivan 1 2018 On spectral gaps of a Laplacian in a strip with a bounded periodic perturbation. Zbl 1463.35386 Borisov, Denis Ivanovich 1 2018 Scale-free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations. Zbl 1381.35027 Borisov, Denis; Tautenhahn, Martin; Veselić, Ivan 8 2017 On the spectral stability of kinks in 2D Klein-Gordon model with parity-time-symmetric perturbation. Zbl 1364.35305 Borisov, D. I.; Dmitriev, S. V. 6 2017 On eigenvalues of a \(\mathcal{PT}\)-symmetric operator in a thin layer. Zbl 1371.35178 Borisov, Denis I.; Znojil, Miloslav 5 2017 The spectrum of geodesic balls on spherically symmetric manifolds. Zbl 1380.53047 Borisov, Denis; Freitas, Pedro 4 2017 Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve. Zbl 1361.35021 Borisov, Denis; Cardone, Giuseppe; Durante, Tiziana 34 2016 Existence of the stationary solution of a Rayleigh-type equation. Zbl 1408.35118 Borisov, D. I.; Gaydukov, R. K. 5 2016 On the resolvent of multidimensional operators with frequently alternating boundary conditions with the Robin homogenized condition. Zbl 1346.35054 Borisov, D. I.; Sharapov, T. F. 4 2016 Quantum Hamiltonians with weak random abstract perturbation. I: Initial length scale estimate. Zbl 1348.82039 Borisov, Denis; Golovina, Anastasia; Veselić, Ivan 3 2016 Expansion of the almost sure spectrum in the weak disorder regime. Zbl 1331.82026 Borisov, Denis; Hoecker-Escuti, Francisco; Veselić, Ivan 2 2016 Creation of spectral bands for a periodic domain with small windows. Zbl 1342.81143 Borisov, D. I. 2 2016 Mathematical and physical meaning of the crossings of energy levels in \(\mathcal {PT}\)-symmetric systems. Zbl 1402.81149 Borisov, Denis I.; Znojil, Miloslav 1 2016 On the band spectrum of a Schrödinger operator in a periodic system of domains coupled by small windows. Zbl 1319.35134 Borisov, D. I. 9 2015 Multiply degenerate exceptional points and quantum phase transitions. Zbl 1329.81037 Borisov, Denis I.; Ružička, František; Znojil, Miloslav 5 2015 Kink scattering from a parity-time-symmetric defect in the \(\phi^4\) model. Zbl 1510.35186 Saadatmand, Danial; Dmitriev, Sergey V.; Borisov, Denis I.; Kevrekidis, Panayotis G.; Fatykhov, Minnekhan A.; Javidan, Kurosh 5 2015 Multiscale unique continuation properties of eigenfunctions. Zbl 1337.35031 Borisov, Denis; Nakić, Ivica; Rose, Christian; Tautenhahn, Martin; Veselić, Ivan 2 2015 Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators. Zbl 1339.81037 Borisov, D.; Tautenhahn, M.; Veselić, I. 2 2015 Perturbation of threshold of essential spectrum for waveguides with windows. II: Asymptotics. Zbl 1335.35162 Borisov, D. I. 1 2015 Perturbation of threshold of essential spectrum for waveguides with windows. I: Decreasing resonance solutions. Zbl 1325.35119 Borisov, D. I. 1 2015 Norm-resolvent convergence for elliptic operators in domain with perforation along curve. Zbl 1304.35058 Borisov, Denis; Cardone, Giuseppe; Durante, Tiziana 3 2014 Waveguide with non-periodically alternating Dirichlet and Robin conditions: Homogenization and asymptotics. Zbl 1282.35033 Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe 29 2013 Uniform resolvent convergence for strip with fast oscillating boundary. Zbl 1286.35025 Borisov, Denis; Cardone, Giuseppe; Faella, Luisa; Perugia, Carmen 24 2013 Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones. Zbl 1269.81050 Borisov, Denis; Pankrashkin, Konstantin 20 2013 Gap opening and split band edges in waveguides coupled by a periodic system of small windows. Zbl 1288.81046 Borisov, D. I.; Pankrashkin, K. V. 18 2013 Low lying eigenvalues of randomly curved quantum waveguides. Zbl 1292.81051 Borisov, Denis; Veselić, Ivan 9 2013 Tunneling resonances in systems without a classical trapping. Zbl 1280.81035 Borisov, D.; Exner, P.; Golovina, A. 8 2013 On a \(\mathcal{PT}\)-symmetric waveguide with a pair of small holes. Zbl 1321.47166 Borisov, D. I. 6 2013 Asymptotics for the expected lifetime of Brownian motion on thin domains in \(\mathbb R^n\). Zbl 1296.60220 Borisov, Denis; Freitas, Pedro 5 2013 On the extrema of band functions in periodic waveguides. Zbl 1308.34111 Borisov, D. I.; Pankrashkin, K. V. 5 2013 On the spectrum of deformations of compact double-sided flat hypersurfaces. Zbl 1282.35261 Borisov, Denis; Freitas, Pedro 2 2013 The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions. Zbl 1241.47042 Borisov, Denis; Krejčiřík, David 11 2012 Planar waveguide with “twisted” boundary conditions: small width. Zbl 1274.81108 Borisov, Denis; Cardone, Giuseppe 6 2012 Homogenization and asymptotics for a waveguide with an infinite number of closely located small windows. Zbl 1290.81038 Borisov, D.; Bunoiu, R.; Cardone, G. 14 2011 Planar waveguide with ”twisted” boundary conditions: Discrete spectrum. Zbl 1273.81100 Borisov, Denis; Cardone, Giuseppe 10 2011 On a waveguide with an infinite number of small windows. (Sur un guide d’onde avec un nombre infini de petites fentes.) Zbl 1211.35098 Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe 10 2011 Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods. Zbl 1223.35248 Borisov, Denis; Cardone, Giuseppe 9 2011 On the spectrum of a two-dimensional periodic operator with a small localized perturbation. Zbl 1233.35066 Borisov, D. I. 9 2011 Low lying spectrum of weak-disorder quantum waveguides. Zbl 1208.82089 Borisov, Denis; Veselić, Ivan 9 2011 Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in \(\mathbb R^d\). Zbl 1180.35397 Borisov, Denis; Freitas, Pedro 32 2010 On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition. Zbl 1210.82077 Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe 26 2010 Homogenization of the planar waveguide with frequently alternating boundary conditions. Zbl 1178.81088 Borisov, D.; Cardone, G. 30 2009 Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains. Zbl 1168.35401 Borisov, Denis; Freitas, Pedro 29 2009 Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation. Zbl 1181.35151 Borisov, Denis; Freitas, Pedro 13 2009 Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients. Zbl 1206.35029 Borisov, D. 12 2009 \(\mathcal {PT}\)-symmetric waveguides. Zbl 1178.35141 Borisov, Denis; Krejčiřík, David 26 2008 On the spectrum of a periodic operator with a small localized perturbation. Zbl 1169.34056 Borisov, D. I.; Gadyl’shin, R. R. 16 2008 Distant perturbations of the Laplacian in a multi-dimensional space. Zbl 1143.35075 Borisov, Denis I. 15 2007 Asymptotic behaviour of the spectrum of a waveguide with distant perturbations. Zbl 1185.35155 Borisov, Denis 14 2007 The spectrum of two quantum layers coupled by a window. Zbl 1115.81024 Borisov, D. 8 2007 Some singular perturbations of periodic operators. Zbl 1147.34060 Borisov, D. I. 7 2007 The spectrum of a self-adjoint differential operator with rapidly oscillating coefficients on the axis. Zbl 1137.34039 Borisov, D. I.; Gadyl’shin, R. R. 4 2007 The spectrum of a periodic operator with a small localized perturbation. Zbl 1175.34106 Borisov, D. I.; Gadyl’shin, R. R. 1 2007 Discrete spectrum of an asymmetric pair of waveguides coupled through a window. Zbl 1156.35066 Borisov, D. I. 31 2006 Distant perturbation asymptotics in window-coupled waveguides. I: The nonthreshold case. Zbl 1112.81043 Borisov, D.; Exner, P. 10 2006 The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential. Zbl 1177.34107 Borisov, D. I.; Gadyl’shin, R. R. 6 2006 On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets. Zbl 1210.34071 Borisov, D. I. 3 2006 On the spectrum of the Schrödinger operator perturbed by a rapidly oscillating potential. Zbl 1134.34337 Borisov, D. I. 2 2006 Spectrum of the magnetic Schrödinger operator in a waveguide with combined boundary conditions. Zbl 1077.81038 Borisov, Denis; Ekholm, Tomas; Kovařík, Hynek 11 2005 Discrete spectrum of the Schrödinger operator perturbed by a narrowly supported potential. Zbl 1178.35144 Bikmetov, A. R.; Borisov, D. I. 1 2005 Exponential splitting of bound states in a waveguide with a pair of distant windows. Zbl 1050.81008 Borisov, D.; Exner, P. 20 2004 Asymptotics and estimates of the convergence rate in a three-dimensional boundary value problem with rapidly alternating boundary conditions. Zbl 1108.35032 Borisov, D. I. 4 2004 On a model boundary value problem for Laplacian with frequently alternating type of boundary condition. Zbl 1137.35308 Borisov, Denis I. 17 2003 Asymptotics and estimates for the eigenelements of the Laplacian with frequent nonperiod change of boundary conditions. Zbl 1067.35055 Borisov, D. I. 12 2003 Geometric coupling thresholds in a two-dimensional strip. Zbl 1060.35094 Borisov, D.; Exner, P.; Gadyl’shin, R. 29 2002 Boundary-value problem in a cylinder with frequently changing type of boundary conditions. Zbl 1045.35047 Borisov, D. I. 6 2002 ...and 5 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 272 Authors 80 Borisov, Denis Ivanovich 40 Nazarov, Sergeĭ Aleksandrovich 19 Cardone, Giuseppe 16 Krejčiřík, David 15 Veselić, Ivan 9 Exner, Pavel 9 Golovina, Anastasiya Mihajlovna 8 Chechkin, Gregory Aleksandrovich 8 Gadyl’shin, Rustem R. 8 Verri, Alessandra A. 7 Freitas, Pedro 7 Khrabustovskyi, Andrii 7 Khusnullin, Il’fat Khamzievich 7 Siegl, Petr 7 Zezyulin, Dmitry A. 6 Bikmetov, Aĭdar Renatovich 6 Drouot, Alexis 6 Pérez-martínez, María-eugenia 6 Taskinen, Jari 6 Tautenhahn, Martin 6 Weinstein, Michael I. 6 Yang, Chuanfu 5 Gaydukov, R. K. 5 Gómez, Delfina 5 Konyrkulzhaeva, Maral Nurlanovna 5 Mukhametrakhimova, Albina I. 5 Täufer, Matthias 5 Trynin, Aleksandr Yur’evich 4 Bunoiu, Renata 4 de Oliveira, César R. 4 Kovařík, Hynek 4 Lotoreichik, Vladimir 4 Najar, Hatem 4 Orive Illera, Rafael 4 Pankrashkin, Konstantin 4 Popov, Igor’ Yur’evich 4 Znojil, Miloslav 3 Barseghyan, Diana 3 Beck, Thomas L. 3 Buttazzo, Giuseppe 3 Chechkina, Aleksandra Grigorievna 3 De Maio, Umberto 3 Durante, Tiziana 3 Fefferman, Charles Louis 3 Grushin, V. V. 3 Kondej, Sylwia 3 Laugesen, Richard Snyder 3 Pažanin, Igor 3 Raymond, Nicolas 3 Royer, Julien 3 Ruotsalainen, Keijo Matti 3 Senik, Nikita N. 3 Siudeja, Bartłomiej Andrzej 3 Suslina, Tat’yana Aleksandrovna 2 Aiyappan, Srinivasan 2 Alonso Izquierdo, A. Alonso 2 Amorim, Rafael T. 2 Bakharev, Fedor L’vovich 2 Behrndt, Jussi 2 Berkolaiko, Gregory 2 Briani, Luca 2 Briet, Philippe 2 D’Apice, Ciro 2 Dittrich, Jaroslav 2 Duchêne, Vincent 2 Ekholm, Tomas 2 Faella, Luisa 2 Hıra, Fatma 2 Hoecker-Escuti, Francisco 2 Koroleva, Yulia O. 2 Langer, Matthias 2 Lee-Thorp, James P. 2 Lu, Jianfeng 2 Marušić-Paloka, Eduard 2 Marzuola, Jeremy Louis 2 Mascarenhas, Maria-Luisa 2 Mitrokhin, Sergeĭ Ivanovich 2 Nieto, Luis Miguel 2 Perugia, Carmen 2 Piatnitski, Andrey L. 2 Plum, Michael 2 Podolskii, Alexander V. 2 Prinari, Francesca 2 Queiroga-Nunes, J. 2 Raikov, Georgi D. 2 Rybalko, Yan 2 Schneider, Baruch 2 Shaposhnikova, Tatiana A. 2 Sharapov, Timur Farkhatovich 2 Shepelsky, Dmitry 2 Uusitalo, Pauliina 2 Vukićević, Iva 2 Wang, Juan 2 Watson, Alexander B. 2 Železný, Jakub 2 Zhao, Jie 1 Akbarfam, Aliasghar Jodayree 1 Akhmetgaliyev, Eldar 1 Alkhutov, Yuriy Alexandrovich 1 Altinisik, Nihat ...and 172 more Authors all top 5 Cited in 118 Serials 32 Journal of Mathematical Sciences (New York) 18 Journal of Mathematical Physics 14 Journal of Mathematical Analysis and Applications 14 Journal of Differential Equations 11 Russian Journal of Mathematical Physics 10 Mathematical Notes 9 Journal of Physics A: Mathematical and Theoretical 8 Journal of Functional Analysis 8 SIAM Journal on Mathematical Analysis 8 St. Petersburg Mathematical Journal 7 Theoretical and Mathematical Physics 7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 7 Ufimskiĭ Matematicheskiĭ Zhurnal 6 Annales Henri Poincaré 6 Journal of Spectral Theory 5 Applicable Analysis 5 Journal of Statistical Physics 5 Reports on Mathematical Physics 5 Journal de Mathématiques Pures et Appliquées. 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Real World Applications 1 Communications on Pure and Applied Analysis 1 Vladikavkazskiĭ Matematicheskiĭ Zhurnal ...and 18 more Serials all top 5 Cited in 30 Fields 251 Partial differential equations (35-XX) 112 Quantum theory (81-XX) 91 Operator theory (47-XX) 50 Ordinary differential equations (34-XX) 32 Statistical mechanics, structure of matter (82-XX) 24 Optics, electromagnetic theory (78-XX) 19 Global analysis, analysis on manifolds (58-XX) 18 Mechanics of deformable solids (74-XX) 17 Calculus of variations and optimal control; optimization (49-XX) 9 Dynamical systems and ergodic theory (37-XX) 9 Fluid mechanics (76-XX) 8 Approximations and expansions (41-XX) 7 Probability theory and stochastic processes (60-XX) 7 Numerical analysis (65-XX) 5 Combinatorics (05-XX) 5 Differential geometry (53-XX) 4 Algebraic geometry (14-XX) 4 Difference and functional equations (39-XX) 4 Functional analysis (46-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 Number theory (11-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 2 Integral equations (45-XX) 2 Relativity and gravitational theory (83-XX) 2 Systems theory; control (93-XX) 1 Potential theory (31-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year