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, “Spectral asymptotics for the one-dimensional Schrodinger operator on an interval with a shift in the free term and the Dirichlet boundary condition”, Izv. RAN. Ser. Mat., 89:3 (2025), 23–44      
2. D. I. Borisov, D. M. Polyakov, “Spectral asymptotics for Schrödinger operator perturbed by translation operator”, Izv. Math., 89:3 (2025), 442–460        
3. D. I. Borisov, D. M. Polyakov, “Asymptotics for Eigenvalues of Schrödinger Operator with Small Translation and Dirichlet Condition”, Dokl. Math., 2024  
4. 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          
5. 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    
6. 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    
7. Dmitry M. Polyakov, “Eigenvalue Asymptotics and a Trace Formula for a Fourth-Order Differential Operator”, Complex Anal. Oper. Theory, 17:8 (2023)  
8. 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  
9. Dmitry M. Polyakov, “Spectral analysis of an even order differential operator with square integrable potential”, Math Methods in App Sciences, 46:5 (2023), 5483  
10. 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    
11. D. M. Polyakov, “Spectral estimates for fourth-order differential operator with periodic coefficients”, Russian Math. (Iz. VUZ), 66:7 (2022), 76–81      
12. D. M. Polyakov, “Spectral Asymptotics of Two-Term Even Order Operators with Involution”, J Math Sci, 260:6 (2022), 806  
13. Dmitry M. Polyakov, “Sharp eigenvalue asymptotics of fourth-order differential operators”, ASY, 130:3-4 (2022), 477  
14. 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    
15. D. M. Polyakov, “Spectral estimates for the fourth-order operator with matrix coefficients”, Comput. Math. Math. Phys., 60:7 (2020), 1163–1184          
16. D. M. Polyakov, “Formula for Regularized Trace of a Second Order Differential Operator with Involution”, J Math Sci, 251:5 (2020), 748  
17. D. M. Polyakov, “On the Spectral Characteristics of Non-Self-Adjoint Fourth-Order Operators with Matrix Coefficients”, Math. Notes, 105:4 (2019), 630–635            
18. S. I. Mitrokhin, “Asimptotika spektra periodicheskoi kraevoi zadachi dlya differentsialnogo operatora s summiruemym potentsialom”, Tr. IMM UrO RAN, 25, no. 1, 2019, 136–149      
19. N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405      
20. 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        
21. D. M. Polyakov, “A one-dimensional Schrödinger operator with square-integrable potential”, Siberian Math. J., 59:3 (2018), 470–485          
22. 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      
23. 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                
24. A. G. Baskakov, D. M. Polyakov, “Spectral Properties of the Hill Operator”, Math. Notes, 99:4 (2016), 598–602            
25. Polyakov D.M., “Spectral properties of an even-order differential operator”, Differ. Equ., 52:8 (2016), 1098–1103