01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
28.01.1951
E-mail:
Keywords:
differential and difference operators, asymptotics for solutions of differential and difference equations, generalized Jacobi matrices, deficiency index of simmetric operators, defect numbers, spectrum.
Limit point ndash; limit circle for differential and difference operators. Asymptotics for solutions of linear ordinary differential and difference equations. deficiency index of simmetric operators. Problems of self-adjoint extensions of singular and irregular differential operators.
Main publications:
Kostuchenko A. G., Mirzoev K. A. Generalized Jacobi matrices and deficiency index of ordinary differential operators with polinomial coefficients // Functional analysis and applications, 1999, v. 33, no. 1, p. 30–45.
Dolgikh I. N., Mirzoev K. A. Deficiensy indices and spectrum of self-adjoint extensions of some classes of differential operators // Sbornik: Mathematics, 2006, v. 197, no. 4, p. 525–546.
Mirzoev K. A., Konechnaya N. N. On a class of operators related to second-order differential equations // Russian Journal of Mathematical Physics, 2006, v. 13, no. 1, p. 55&ndsh;63.
Mirzoev K. A., Eastham M. S. P. A Liouville–Green asymptotic estimate for a class of differential systems // Russian Journal of Mathematical Physics, 2005, v. 12, no. 4, p. 439–442.
Mirzoev K. A. About analogues of limit point's theorems for quasidifferential equations of high order // Doklady Mathematics, 1994, v. 338, no. 3, p. 306–309.
Mirzoev K. A. Orlov's theorem on the deficiency index of differential operators // Doklady Mathematics, 2001, v. 64, no. 2, p.591–595.
K. A. Mirzoev, T. A. Safonova, “Lacunary Recurrence Relations with Gaps of Length 8 for the Bernoulli and Euler Polynomials”, Mat. Zametki, 115:2 (2024), 308–313; Math. Notes, 115:2 (2024), 279–284
2023
2.
K. A. Mirzoev, T. A. Safonova, “Around the Gauss theorem on the values of Euler's digamma function at rational points”, Algebra i Analiz, 35:2 (2023), 86–106; St. Petersburg Math. J., 35:2 (2024), 311–325
N. N. Konechnaja, K. A. Mirzoev, A. A. Shkalikov, “Asymptotics of Solutions of Two-Term Differential Equations”, Mat. Zametki, 113:2 (2023), 217–235; Math. Notes, 113:2 (2023), 228–242
K. A. Mirzoev, T. A. Safonova, “Polynomials in the differentiation operator and formulas for the sums of some converging series”, Funktsional. Anal. i Prilozhen., 56:1 (2022), 81–93; Funct. Anal. Appl., 56:1 (2022), 61–71
K. A. Mirzoev, T. A. Safonova, “Values of the Riemann Zeta Function and the Dirichlet Beta Function at Positive Integer Points and Multiple Numerical Series”, Mat. Zametki, 112:6 (2022), 947–952; Math. Notes, 112:6 (2022), 1071–1076
2021
6.
V. Budyka, M. Malamud, K. Mirzoev, “Deficiency indices of block Jacobi matrices: survey”, CMFD, 67:2 (2021), 237–254
K. A. Mirzoev, T. A. Safonova, “Integral Representation of Sums of Series Associated with Special Functions”, Mat. Zametki, 108:4 (2020), 632–637; Math. Notes, 108:4 (2020), 617–622
K. A. Mirzoev, N. N. Konechnaja, “Asymptotics of solutions to linear differential equations of odd order”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020, no. 1, 23–28; Moscow University Mathematics Bulletin, 75:1 (2020), 22–26
K. A. Mirzoev, T. A. Safonova, “Ordinary differential operators and the integral representation of sums of certain power series”, Tr. Mosk. Mat. Obs., 80:2 (2019), 157–177; Trans. Moscow Math. Soc., 80 (2019), 133–151
K. A. Mirzoev, T. A. Safonova, “On Integral Representation of Sums of Some Power Series”, Mat. Zametki, 106:3 (2019), 470–475; Math. Notes, 106:3 (2019), 468–472
N. N. Konechnaja, K. A. Mirzoev, “The Leading Term of the Asymptotics of Solutions of Linear Differential Equations with First-Order Distribution Coefficients”, Mat. Zametki, 106:1 (2019), 74–83; Math. Notes, 106:1 (2019), 81–88
I. N. Braeutigam, K. A. Mirzoev, “On the defect numbers of operators generated by Jacobian matrices with operator entries”, Algebra i Analiz, 30:4 (2018), 1–26; St. Petersburg Math. J., 30:4 (2019), 621–638
K. A. Mirzoev, N. N. Konechnaja, T. A. Safonova, R. N. Tagirova, “Generalized Jacobian Matrices and Spectral Analysis of Differential Operators with Polynomial Coefficients”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 152 (2018), 91–102; J. Math. Sci. (N. Y.), 252:2 (2021), 213–224
N. N. Konechnaja, K. A. Mirzoev, A. A. Shkalikov, “On the Asymptotic Behavior of Solutions to Two-Term Differential Equations with Singular Coefficients”, Mat. Zametki, 104:2 (2018), 231–242; Math. Notes, 104:2 (2018), 244–252
I. N. Braeutigam, K. A. Mirzoev, “Asymptotics of Solutions of Matrix Differential Equations with Nonsmooth Coefficients”, Mat. Zametki, 104:1 (2018), 148–153; Math. Notes, 104:1 (2018), 150–155
K. A. Mirzoev, N. N. Konechnaja, T. A. Safonova, R. N. Tagirova, “On asymptotics of solutions to some linear differential equations”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 141 (2017), 103–110; Journal of Mathematical Sciences, 241:5 (2019), 614–621
N. N. Konechnaya, K. A. Mirzoev, “Asymptotics of solutions to a class of linear differential equations”, Ufimsk. Mat. Zh., 9:3 (2017), 78–88; Ufa Math. J., 9:3 (2017), 76–86
18.
I. N. Braeutigam, K. A. Mirzoev, T. A. Safonova, “On deficiency index for some second order vector differential operators”, Ufimsk. Mat. Zh., 9:1 (2017), 18–28; Ufa Math. J., 9:1 (2017), 18–28
K. A. Mirzoev, N. N. Konechnaja, “Asymptotics of Solutions of a Class of Linear Differential Equations with Nonsmooth Coefficients”, Mat. Zametki, 100:2 (2016), 312–317; Math. Notes, 100:2 (2016), 334–340
K. A. Mirzoev, A. A. Shkalikov, “Differential Operators of Even Order with Distribution Coefficients”, Mat. Zametki, 99:5 (2016), 788–793; Math. Notes, 99:5 (2016), 779–784
K. A. Mirzoev, T. A. Safonova, “On the Deficiency Index of the Vector-Valued Sturm–Liouville Operator”, Mat. Zametki, 99:2 (2016), 262–277; Math. Notes, 99:2 (2016), 290–303
I. N. Braeutigam, K. A. Mirzoev, T. A. Safonova, “An Analog of Orlov's Theorem on the Deficiency Index of Second-Order Differential Operators”, Mat. Zametki, 97:2 (2015), 314–317; Math. Notes, 97:2 (2015), 300–303
K. A. Mirzoev, T. A. Safonova, “The singular Sturm–Liouville operators with nonsmooth potentials in a space of vector functions”, Ufimsk. Mat. Zh., 3:3 (2011), 105–119
I. N. Dolgikh, K. A. Mirzoev, “Deficiency indices and spectrum of self-adjoint extensions of some classes of differential operators”, Mat. Sb., 197:4 (2006), 53–74; Sb. Math., 197:4 (2006), 525–546
A. G. Kostyuchenko, K. A. Mirzoev, “Complete Indefiniteness Tests for Jacobi Matrices with Matrix Entries”, Funktsional. Anal. i Prilozhen., 35:4 (2001), 32–37; Funct. Anal. Appl., 35:4 (2001), 265–269
K. A. Mirzoev, “On a class of operators connected with second-order differential equations”, Uspekhi Mat. Nauk, 55:6(336) (2000), 147–148; Russian Math. Surveys, 55:6 (2000), 1159–1160
A. G. Kostyuchenko, K. A. Mirzoev, “Generalized Jacobi Matrices and Deficiency Numbers of Ordinary Differential Operators with Polynomial Coefficients”, Funktsional. Anal. i Prilozhen., 33:1 (1999), 30–45; Funct. Anal. Appl., 33:1 (1999), 25–37
A. G. Kostyuchenko, K. A. Mirzoev, “Three-term recurrence relations with matrix coefficients. The completely indefinite case”, Mat. Zametki, 63:5 (1998), 709–716; Math. Notes, 63:5 (1998), 624–630
K. A. Mirzoev, “$L^p$-Properties of Solutions to Quasi-Differential Equations and Perturbation of Their Coefficients on Sets of Positive Measure”, Funktsional. Anal. i Prilozhen., 31:1 (1997), 80–83; Funct. Anal. Appl., 31:1 (1997), 63–64
A. G. Kostyuchenko, K. A. Mirzoev, “A criterion for the complete indeterminacy of three-term recurrence relations”, Uspekhi Mat. Nauk, 51:6(312) (1996), 207–208; Russian Math. Surveys, 51:6 (1996), 1208–1209
K. A. Mirzoev, “Analogues of limit point theorems for higher-order
quasidifferential equations”, Dokl. Akad. Nauk, 338:3 (1994), 306–309; Dokl. Math., 50:2 (1995), 245–250
1992
35.
K. A. Mirzoev, “On a generalization of Eastham's theorem on a limit point”, Uspekhi Mat. Nauk, 47:4(286) (1992), 203–204; Russian Math. Surveys, 47:4 (1992), 222–223
K. A. Mirzoev, “Existence conditions for solutions of quasidifferential equations which do not belong to the space $\mathscr L^p(0,+\infty)$”, Mat. Zametki, 50:6 (1991), 105–115; Math. Notes, 50:6 (1991), 1287–1294
K. A. Mirzoev, “The Cauchy function and $\mathscr{L}^p_w$-properties of solutions of quasidifferential equations”, Uspekhi Mat. Nauk, 46:4(280) (1991), 161–162; Russian Math. Surveys, 46:4 (1991), 190–191
K. A. Mirzoev, “Conditions for the existence of a solution to the equation $y''=qy$ that does not belong to the space $\mathscr{L}^p(0,+\infty)$”, Mat. Zametki, 47:4 (1990), 77–82; Math. Notes, 47:4 (1990), 364–368
K. A. Mirzoev, “A criterion for the quasi-regularity of an operator induced by a quasi-differential expression”, Uspekhi Mat. Nauk, 40:1(241) (1985), 207–208; Russian Math. Surveys, 40:1 (1985), 229–230
A. I. Aptekarev, A. M. Akhtyamov, O. V. Besov, A. A. Vladimirov, B. S. Kashin, K. A. Mirzoev, S. N. Naboko, R. O. Oinarov, I. V. Sadovnichaya, A. M. Savchuk, A. G. Sergeev, V. D. Stepanov, Ya. T. Sultanaev, D. V. Treschev, I. A. Sheipak, “Andrei Andreevich Shkalikov (on his seventieth birthday)”, Tr. Mosk. Mat. Obs., 80:2 (2019), 133–145; Trans. Moscow Math. Soc., 80 (2019), 113–122
Вокруг теоремы Гаусса о значениях дигамма-функции Эйлера
в рациональных точках K. A. Mirzoev, T. A. Safonova XXI International Conference «Algebra, Number Theory, Discrete Geometry and Multiscale Modeling: Modern Problems, Applications and Problems of History», Dedicated to the 85th Anniversaryof the Birth of A. A. Karatsuba May 19, 2022 13:05
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