Eckhardt, Jonathan; Kostenko, Aleksey On the absolutely continuous spectrum of generalized indefinite strings. (English) Zbl 07432933 Ann. Henri Poincaré 22, No. 11, 3529-3564 (2021). Reviewer: Dmitry Shepelsky (Kharkov) MSC: 34L05 34B07 34B20 34L25 PDF BibTeX XML Cite \textit{J. Eckhardt} and \textit{A. Kostenko}, Ann. Henri Poincaré 22, No. 11, 3529--3564 (2021; Zbl 07432933) Full Text: DOI arXiv OpenURL
Fucci, Guglielmo; Gesztesy, Fritz; Kirsten, Klaus; Stanfill, Jonathan Spectral \(\zeta\)-functions and \(\zeta\)-regularized functional determinants for regular Sturm-Liouville operators. (English) Zbl 07423435 Res. Math. Sci. 8, No. 4, Paper No. 61, 46 p. (2021). MSC: 47A10 47B10 47G10 34B27 34L40 PDF BibTeX XML Cite \textit{G. Fucci} et al., Res. Math. Sci. 8, No. 4, Paper No. 61, 46 p. (2021; Zbl 07423435) Full Text: DOI arXiv OpenURL
Sukhanov, V. V. Trace formulas for the one-dimensional Stark operator and integrals of motion for the cylindrical Korteweg-de Vries equation. (English. Russian original) Zbl 1453.34108 St. Petersbg. Math. J. 31, No. 5, 903-910 (2020); translation from Algebra Anal. 31, No. 5, 206-215 (2019). MSC: 34L05 34A55 34L40 34A05 PDF BibTeX XML Cite \textit{V. V. Sukhanov}, St. Petersbg. Math. J. 31, No. 5, 903--910 (2020; Zbl 1453.34108); translation from Algebra Anal. 31, No. 5, 206--215 (2019) Full Text: DOI OpenURL
Takhtajan, Leon A. Etudes of the resolvent. (English. Russian original) Zbl 1440.47004 Russ. Math. Surv. 75, No. 1, 147-186 (2020); translation from Usp. Mat. Nauk 75, No. 1, 155-194 (2020). Reviewer: Khristo N. Boyadzhiev (Ada) MSC: 47A10 47B25 34B24 35P10 47-02 PDF BibTeX XML Cite \textit{L. A. Takhtajan}, Russ. Math. Surv. 75, No. 1, 147--186 (2020; Zbl 1440.47004); translation from Usp. Mat. Nauk 75, No. 1, 155--194 (2020) Full Text: DOI arXiv OpenURL
Korotyaev, Evgeny Trace formulas for Schrödinger operators with complex potentials on a half line. (English) Zbl 1442.47032 Lett. Math. Phys. 110, No. 1, 1-20 (2020). Reviewer: Guy Katriel (Haifa) MSC: 47E05 34L20 34L40 81Q10 PDF BibTeX XML Cite \textit{E. Korotyaev}, Lett. Math. Phys. 110, No. 1, 1--20 (2020; Zbl 1442.47032) Full Text: DOI arXiv OpenURL
Gesztesy, Fritz; Kirsten, Klaus Effective computation of traces, determinants, and \(\zeta\)-functions for Sturm-Liouville operators. (English) Zbl 06988448 J. Funct. Anal. 276, No. 2, 520-562 (2019). MSC: 47A10 47B10 47G10 34B27 34L40 PDF BibTeX XML Cite \textit{F. Gesztesy} and \textit{K. Kirsten}, J. Funct. Anal. 276, No. 2, 520--562 (2019; Zbl 06988448) Full Text: DOI arXiv OpenURL
Yafaev, D. R. Analytic scattering theory for Jacobi operators and Bernstein-Szegö asymptotics of orthogonal polynomials. (English) Zbl 1405.33014 Rev. Math. Phys. 30, No. 8, Article ID 1840019, 47 p. (2018). MSC: 33C45 39A70 47A40 47B39 PDF BibTeX XML Cite \textit{D. R. Yafaev}, Rev. Math. Phys. 30, No. 8, Article ID 1840019, 47 p. (2018; Zbl 1405.33014) Full Text: DOI OpenURL
Usman, Muhammad; Zaidi, Ali Ashher Trace formulas for Schrödinger operators on star graphs with general matching conditions. (English) Zbl 1397.81075 J. Phys. A, Math. Theor. 51, No. 36, Article ID 365301, 18 p. (2018). MSC: 81Q35 05C12 81Q10 34L40 PDF BibTeX XML Cite \textit{M. Usman} and \textit{A. A. Zaidi}, J. Phys. A, Math. Theor. 51, No. 36, Article ID 365301, 18 p. (2018; Zbl 1397.81075) Full Text: DOI OpenURL
Demirel-Frank, Semra; Shou, Laura Trace formulas for Schrödinger operators on star graphs. (English) Zbl 1387.81222 Bull. Math. Sci. 8, No. 1, 15-31 (2018). MSC: 81Q35 81Q05 81Q10 35J10 PDF BibTeX XML Cite \textit{S. Demirel-Frank} and \textit{L. Shou}, Bull. Math. Sci. 8, No. 1, 15--31 (2018; Zbl 1387.81222) Full Text: DOI arXiv OpenURL
Takhtajan, Leon A.; Alekseev, Anton Yu.; Aref’eva, Irina Ya.; Semenov-Tian-Shansky, Michael A.; Sklyanin, Evgeny K.; Smirnov, Fedor A.; Shatashvili, Samson L. Scientific heritage of L. D. Faddeev. Survey of papers. (English. Russian original) Zbl 1396.81008 Russ. Math. Surv. 72, No. 6, 977-1081 (2017); translation from Usp. Mat. Nauk 72, No. 6, xx (2017). MSC: 81-03 01A60 01A70 16T25 17B37 35J10 35P25 35Q53 35Q55 37K15 58B32 58J52 70S15 81R50 81S40 81T10 81T13 81T50 81T70 81U40 82B23 82C23 PDF BibTeX XML Cite \textit{L. A. Takhtajan} et al., Russ. Math. Surv. 72, No. 6, 977--1081 (2017; Zbl 1396.81008); translation from Usp. Mat. Nauk 72, No. 6, xx (2017) Full Text: DOI OpenURL
Weder, Ricardo Trace formulas for the matrix Schrödinger operator on the half-line with general boundary conditions. (English) Zbl 1351.81050 J. Math. Phys. 57, No. 11, 112101, 11 p. (2016). MSC: 81Q10 34L40 PDF BibTeX XML Cite \textit{R. Weder}, J. Math. Phys. 57, No. 11, 112101, 11 p. (2016; Zbl 1351.81050) Full Text: DOI arXiv OpenURL
Schimmer, Lukas Spectral inequalities for Jacobi operators and related sharp Lieb-Thirring inequalities on the continuum. (English) Zbl 1317.35155 Commun. Math. Phys. 334, No. 1, 473-505 (2015). Reviewer: Leonid Golinskii (Kharkov) MSC: 35P15 47B36 PDF BibTeX XML Cite \textit{L. Schimmer}, Commun. Math. Phys. 334, No. 1, 473--505 (2015; Zbl 1317.35155) Full Text: DOI arXiv OpenURL
Yafaev, D. R. Spectral and scattering theory for perturbations of the Carleman operator. (English. Russian original) Zbl 1320.47005 St. Petersbg. Math. J. 25, No. 2, 339-359 (2014); translation from Algebra Anal. 25, No. 2, 251-278 (2013). Reviewer: Vladimir V. Peller (East Lansing) MSC: 47A40 47B25 47B35 PDF BibTeX XML Cite \textit{D. R. Yafaev}, St. Petersbg. Math. J. 25, No. 2, 339--359 (2014; Zbl 1320.47005); translation from Algebra Anal. 25, No. 2, 251--278 (2013) Full Text: DOI arXiv OpenURL
Babich, V. M.; Budylin, A. M.; Dmitrieva, L. A.; Fedotov, A. A.; Komech, A. I.; Levin, S. B.; Perel, M. V.; Rybakina, E. A.; Sukhanov, V. V. On the mathematical work of Vladimir Savel’evich Buslaev. (English. Russian original) Zbl 1304.35001 St. Petersbg. Math. J. 25, No. 2, 151-174 (2014); translation from Algebra Anal. 25, No. 2, 3-36 (2013). MSC: 35-00 01A70 PDF BibTeX XML Cite \textit{V. M. Babich} et al., St. Petersbg. Math. J. 25, No. 2, 151--174 (2014; Zbl 1304.35001); translation from Algebra Anal. 25, No. 2, 3--36 (2013) Full Text: DOI OpenURL
Gesztesy, Fritz; Nichols, Roger Weak convergence of spectral shift functions for one-dimensional Schrödinger operators. (English) Zbl 1263.47026 Math. Nachr. 285, No. 14-15, 1799-1838 (2012). Reviewer: Bilender P. Allahverdiev (Isparta) MSC: 47B25 34L05 34L25 34L40 34B24 34B27 47E05 PDF BibTeX XML Cite \textit{F. Gesztesy} and \textit{R. Nichols}, Math. Nachr. 285, No. 14--15, 1799--1838 (2012; Zbl 1263.47026) Full Text: DOI arXiv OpenURL
Borovyk, Vita; Makarov, Konstantin A. On the weak and ergodic limit of the spectral shift function. (English) Zbl 1243.81077 Lett. Math. Phys. 100, No. 1, 1-15 (2012). MSC: 81Q10 35P20 47N50 81U30 35J10 PDF BibTeX XML Cite \textit{V. Borovyk} and \textit{K. A. Makarov}, Lett. Math. Phys. 100, No. 1, 1--15 (2012; Zbl 1243.81077) Full Text: DOI arXiv OpenURL
Isozaki, Hiroshi; Korotyaev, Evgeny Inverse problems, trace formulae for discrete Schrödinger operators. (English) Zbl 1250.81124 Ann. Henri Poincaré 13, No. 4, 751-788 (2012). MSC: 81U40 81Q05 81Q10 65N22 PDF BibTeX XML Cite \textit{H. Isozaki} and \textit{E. Korotyaev}, Ann. Henri Poincaré 13, No. 4, 751--788 (2012; Zbl 1250.81124) Full Text: DOI arXiv Link OpenURL
Demirel, Semra; Usman, Muhammad Trace formulas for Schrödinger operators on the half-line. (English) Zbl 1256.35041 Bull. Math. Sci. 1, No. 2, 397-427 (2011). MSC: 35P25 35Q41 81Q05 PDF BibTeX XML Cite \textit{S. Demirel} and \textit{M. Usman}, Bull. Math. Sci. 1, No. 2, 397--427 (2011; Zbl 1256.35041) Full Text: DOI arXiv OpenURL
Pushnitski, Alexander Scattering matrix and functions of self-adjoint operators. (English) Zbl 1244.47013 J. Spectr. Theory 1, No. 2, 221-236 (2011). Reviewer: Shuji Watanabe (Maebashi) MSC: 47A40 47B25 PDF BibTeX XML Cite \textit{A. Pushnitski}, J. Spectr. Theory 1, No. 2, 221--236 (2011; Zbl 1244.47013) Full Text: DOI arXiv OpenURL
Buslaev, Vladimir; Pushnitski, Alexander The scattering matrix and associated formulas in Hamiltonian mechanics. (English) Zbl 1218.37072 Commun. Math. Phys. 293, No. 2, 563-588 (2010). Reviewer: Yuri E. Gliklikh (Voronezh) MSC: 37J05 37J10 34L25 35P25 81U20 PDF BibTeX XML Cite \textit{V. Buslaev} and \textit{A. Pushnitski}, Commun. Math. Phys. 293, No. 2, 563--588 (2010; Zbl 1218.37072) Full Text: DOI arXiv OpenURL
Pozharskiĭ, A. A. Absolutely continuous spectrum of Stark type operators. (English. Russian original) Zbl 1206.81039 St. Petersbg. Math. J. 20, No. 3, 473-492 (2009); translation from Algebra Anal. 20, No. 3, 197-223 (2008). MSC: 81Q10 34L20 47E05 PDF BibTeX XML Cite \textit{A. A. Pozharskiĭ}, St. Petersbg. Math. J. 20, No. 3, 473--492 (2009; Zbl 1206.81039); translation from Algebra Anal. 20, No. 3, 197--223 (2008) Full Text: DOI OpenURL
Yafaev, D. R. The Schrödinger operator: Perturbation determinants, the spectral shift function, trace identities, and all that. (English) Zbl 1222.47072 Funct. Anal. Appl. 41, No. 3, 217-236 (2007); translation from Funkts. Anal. Prilozh. 41, No. 3, 60-83 (2007). Reviewer: Wolfgang Sprößig (Freiberg) MSC: 47F05 35P20 PDF BibTeX XML Cite \textit{D. R. Yafaev}, Funct. Anal. Appl. 41, No. 3, 217--236 (2007; Zbl 1222.47072); translation from Funkts. Anal. Prilozh. 41, No. 3, 60--83 (2007) Full Text: DOI OpenURL
Pozharskiĭ, A. A. On the spectrum of the Wannier-Stark operator. (English. Russian original) Zbl 1071.81041 St. Petersbg. Math. J. 16, No. 3, 561-581 (2005); translation from Algebra Anal. 16, No. 3, 171-200 (2004). Reviewer: Farruh Mukhamedov (Aveiro) MSC: 81Q10 47E05 34L40 PDF BibTeX XML Cite \textit{A. A. Pozharskiĭ}, St. Petersbg. Math. J. 16, No. 3, 561--581 (2005; Zbl 1071.81041); translation from Algebra Anal. 16, No. 3, 171--200 (2004) Full Text: DOI OpenURL
Bruneau, V.; Pushnitski, A.; Raikov, G. Spectral shift function in strong magnetic fields. (English) Zbl 1082.35115 St. Petersbg. Math. J. 16, No. 1, 181-209 (2004); and Algebra Anal. 16, No. 1, 207-238 (2004). Reviewer: Alexander I. Kheyfits (Bronx) MSC: 35P25 35P20 35J10 81U99 PDF BibTeX XML Cite \textit{V. Bruneau} et al., St. Petersbg. Math. J. 16, No. 1, 181--209 (2004; Zbl 1082.35115) Full Text: DOI OpenURL
Bouclet, Jean-Marc Spectral distributions for long range perturbations. (English) Zbl 1088.35041 J. Funct. Anal. 212, No. 2, 431-471 (2004). Reviewer: Ricardo Weder (México City) MSC: 35P25 35Q40 81Q10 81U20 81U05 35S05 PDF BibTeX XML Cite \textit{J.-M. Bouclet}, J. Funct. Anal. 212, No. 2, 431--471 (2004; Zbl 1088.35041) Full Text: DOI OpenURL
Rybkin, Alexei Necessary and sufficient conditions for absolute summability of the trace formulas for certain one dimensional Schrödinger operators. (English) Zbl 1017.34087 Proc. Am. Math. Soc. 131, No. 1, 219-229 (2003). Reviewer: N.D.Sengupta (Mumbai) MSC: 34L40 47E05 34L25 PDF BibTeX XML Cite \textit{A. Rybkin}, Proc. Am. Math. Soc. 131, No. 1, 219--229 (2003; Zbl 1017.34087) Full Text: DOI OpenURL
Rybkin, Alexei On a complete analysis of high-energy scattering matrix asymptotics for one dimensional Schrödinger operators with integrable potentials. (English) Zbl 0986.34073 Proc. Am. Math. Soc. 130, No. 1, 59-67 (2002). MSC: 34L40 34L25 34L20 PDF BibTeX XML Cite \textit{A. Rybkin}, Proc. Am. Math. Soc. 130, No. 1, 59--67 (2002; Zbl 0986.34073) Full Text: DOI OpenURL
Laptev, Ari; Weidl, Timo Sharp Lieb-Thirring inequalities in high dimensions. (English) Zbl 1142.35531 Acta Math. 184, No. 1, 87-111 (2000). MSC: 35P15 35J10 47F05 81U05 PDF BibTeX XML Cite \textit{A. Laptev} and \textit{T. Weidl}, Acta Math. 184, No. 1, 87--111 (2000; Zbl 1142.35531) Full Text: DOI arXiv OpenURL
Birman, M. Sh.; Pushnitski, A. B. Spectral shift function, amazing and multifaceted. (English) Zbl 0907.47014 Integral Equations Oper. Theory 30, No. 2, 191-199 (1998). MSC: 47B25 47A55 PDF BibTeX XML Cite \textit{M. Sh. Birman} and \textit{A. B. Pushnitski}, Integral Equations Oper. Theory 30, No. 2, 191--199 (1998; Zbl 0907.47014) Full Text: DOI OpenURL
Borisov, N. V.; Il’inskij, K. N. Supersymmetry on noncompact manifolds and complex geometry. (English. Russian original) Zbl 0907.58003 J. Math. Sci., New York 85, No. 1, 1605-1618 (1997); translation from Zap. Nauchn. Semin. POMI 215, 77-99 (1994). MSC: 58C50 81T60 PDF BibTeX XML Cite \textit{N. V. Borisov} and \textit{K. N. Il'inskij}, J. Math. Sci., New York 85, No. 1, 77--99 (1994; Zbl 0907.58003); translation from Zap. Nauchn. Semin. POMI 215, 77--99 (1994) Full Text: DOI EuDML OpenURL
Hinton, D. B.; Klaus, M.; Shaw, J. K. Asymptotic phase, asymptotic modulus, and Titchmarsh-Weyl coefficient for a Dirac system. (English) Zbl 0738.34044 J. Math. Anal. Appl. 142, No. 1, 108-129 (1989). MSC: 34L40 34B20 34L25 34A25 PDF BibTeX XML Cite \textit{D. B. Hinton} et al., J. Math. Anal. Appl. 142, No. 1, 108--129 (1989; Zbl 0738.34044) Full Text: DOI OpenURL
Koplienko, L. S. Regularized spectral shift function for one-dimensional Schrödinger operator with slowly decreasing potential. (English) Zbl 0623.47060 Sib. Math. J. 26, 365-369 (1985). MSC: 47F05 47A10 PDF BibTeX XML Cite \textit{L. S. Koplienko}, Sib. Math. J. 26, 365--369 (1985; Zbl 0623.47060) Full Text: DOI OpenURL
Faddeev, L. D. Inverse problem of quantum scattering theory. II. (English) Zbl 0373.35014 J. Sov. Math. 5, 334-396 (1976). MSC: 81U40 81-02 34Lxx 35P25 47A40 PDF BibTeX XML Cite \textit{L. D. Faddeev}, J. Sov. Math. 5, 334--396 (1976; Zbl 0373.35014) Full Text: DOI OpenURL
McKean, H. P.; van Moerbeke, P. The spectrum of Hill’s equation. (English) Zbl 0319.34024 Invent. Math. 30, 217-274 (1975). MSC: 34L99 34B30 33E05 PDF BibTeX XML Cite \textit{H. P. McKean} and \textit{P. van Moerbeke}, Invent. Math. 30, 217--274 (1975; Zbl 0319.34024) Full Text: DOI EuDML OpenURL
Zakharov, V. E.; Faddeev, L. D. Korteweg-de Vries equation: a completely integrable Hamiltonian system. (English. Russian original) Zbl 0257.35074 Funct. Anal. Appl. 5, 280-287 (1972); translation from Funkts. Anal. Prilozh. 5, No. 4, 18-27 (1971). Reviewer: F. Chorlton MSC: 35Q53 35J10 35P25 PDF BibTeX XML Cite \textit{V. E. Zakharov} and \textit{L. D. Faddeev}, Funct. Anal. Appl. 5, 280--287 (1972; Zbl 0257.35074); translation from Funkts. Anal. Prilozh. 5, No. 4, 18--27 (1971) Full Text: DOI OpenURL
Gilbert, R. C. An asymptotic phase for a Sturm-Liouville operator with unbounded potential. (English) Zbl 0159.11603 Proc. Am. Math. Soc. 18, 967-973 (1967). PDF BibTeX XML Cite \textit{R. C. Gilbert}, Proc. Am. Math. Soc. 18, 967--973 (1967; Zbl 0159.11603) Full Text: DOI OpenURL