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JOURNALS // Algebra i Analiz

Algebra i Analiz, 2015, Volume 27, Issue 5, Pages 117–152 (Mi aa1457)

Spectral analysis of a fourth order differential operator with periodic and antiperiodic boundary conditions
D. M. Polyakov

This publication is cited in the following articles:
  1. D. I. Borisov, D. M. Polyakov, “Asymptotics for Eigenvalues of Schrödinger Operator with Small Translation and Dirichlet Condition”, Dokl. Math., 2024  crossref
  2. D. M. Polyakov, “Spectral asymptotics of a non-self-adjoint fourth-order operator with periodic boundary conditions”, Theoret. and Math. Phys., 221:1 (2024), 1615–1632  mathnet  crossref  crossref  mathscinet  adsnasa
  3. A. G. Baskakov, G. V. Garkavenko, N. B. Uskova, “Primenenie metoda podobnykh operatorov k nekotorym klassam raznostnykh operatorov”, Differentsialnye uravneniya i matematicheskaya fizika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 225, VINITI RAN, M., 2023, 14–27  mathnet  crossref
  4. A. A. Vladimirov, A. A. Shkalikov, “Oscillatory properties of selfadjoint boundary value problems of the fourth order”, St. Petersburg Math. J., 35:1 (2024), 83–100  mathnet  crossref
  5. Dmitry M. Polyakov, “Eigenvalue Asymptotics and a Trace Formula for a Fourth-Order Differential Operator”, Complex Anal. Oper. Theory, 17:8 (2023)  crossref
  6. Dmitry M. Polyakov, “Spectral asymptotics and a trace formula for a fourth-order differential operator corresponding to thin film equation”, Monatsh Math, 202:1 (2023), 171  crossref
  7. Dmitry M. Polyakov, “Spectral analysis of an even order differential operator with square integrable potential”, Math Methods in App Sciences, 46:5 (2023), 5483  crossref
  8. A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “O sglazhivanii operatornogo koeffitsienta differentsialnogo operatora pervogo poryadka v banakhovom prostranstve”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii  i smezhnye problemy», Voronezh, 28 yanvarya – 2 fevralya 2021 g.  Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 206, VINITI RAN, M., 2022, 3–14  mathnet  crossref
  9. D. M. Polyakov, “Spectral estimates for fourth-order differential operator with periodic coefficients”, Russian Math. (Iz. VUZ), 66:7 (2022), 76–81  mathnet  crossref  crossref
  10. D. M. Polyakov, “Spectral Asymptotics of Two-Term Even Order Operators with Involution”, J Math Sci, 260:6 (2022), 806  crossref
  11. Dmitry M. Polyakov, “Sharp eigenvalue asymptotics of fourth-order differential operators”, ASY, 130:3-4 (2022), 477  crossref
  12. G. V. Garkavenko, N. B. Uskova, “O spektralnykh svoistvakh odnoi trekhdiagonalnoi beskonechnoi matritsy”, Materialy 20 Mezhdunarodnoi Saratovskoi zimnei shkoly «Sovremennye problemy teorii funktsii i ikh prilozheniya», Saratov, 28 yanvarya — 1 fevralya 2020 g.  Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 199, VINITI RAN, M., 2021, 31–42  mathnet  crossref
  13. D. M. Polyakov, “Spectral estimates for the fourth-order operator with matrix coefficients”, Comput. Math. Math. Phys., 60:7 (2020), 1163–1184  mathnet  crossref  crossref  isi  elib
  14. D. M. Polyakov, “Formula for Regularized Trace of a Second Order Differential Operator with Involution”, J Math Sci, 251:5 (2020), 748  crossref
  15. D. M. Polyakov, “On the Spectral Characteristics of Non-Self-Adjoint Fourth-Order Operators with Matrix Coefficients”, Math. Notes, 105:4 (2019), 630–635  mathnet  crossref  crossref  mathscinet  isi  elib
  16. S. I. Mitrokhin, “Asimptotika spektra periodicheskoi kraevoi zadachi dlya differentsialnogo operatora s summiruemym potentsialom”, Tr. IMM UrO RAN, 25, no. 1, 2019, 136–149  mathnet  crossref  elib
  17. N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405  mathnet  crossref  mathscinet
  18. I. N. Braeutigam, D. M. Polyakov, “On the asymptotics of eigenvalues of a third-order differential operator”, St. Petersburg Math. J., 31:4 (2020), 585–606  mathnet  crossref  isi  elib
  19. D. M. Polyakov, “A one-dimensional Schrödinger operator with square-integrable potential”, Siberian Math. J., 59:3 (2018), 470–485  mathnet  crossref  crossref  isi  elib
  20. A. G. Baskakov, N. B. Uskova, “Fourier method for first order differential equations with involution and groups of operators”, Ufa Math. J., 10:3 (2018), 11–34  mathnet  crossref  isi
  21. A. G. Baskakov, D. M. Polyakov, “The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential”, Sb. Math., 208:1 (2017), 1–43  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  22. A. G. Baskakov, D. M. Polyakov, “Spectral Properties of the Hill Operator”, Math. Notes, 99:4 (2016), 598–602  mathnet  crossref  crossref  mathscinet  isi  elib
  23. Polyakov D.M., “Spectral properties of an even-order differential operator”, Differ. Equ., 52:8 (2016), 1098–1103  crossref  mathscinet  zmath  isi  elib  scopus


© Steklov Math. Inst. of RAS, 2025