approximation theory; spectral theory of differential operators; asymptotic.
Main publications:
Borzov V. V. Orthogonal polynomials and generalized oscillator algebras // Integral Transforms and Special Functions, 2001, 12, 2, 115–138.
Borzov V. V., Damaskinsky E. V., Kulish P. P. Construction of the spectral measure for deformed oscillator positon operator in the case of undetermined Hamburger moment problem // Review in Math. Phys., 2000, 12, 5, 691–710.
Borzov V. V. On the Limit Distribution of a Homogenous Polynomial on the Unit Sphere of Large Dimension // Amer. Math. Soc. Transl. (2), 1999, 188, 19–45.
Борзов B. B. О высокотемпературной асимптотике статсуммы для Р(Ф)-модели евклидовой теории поля // Теор. матем. физ., 1988, 76, 3, 322–338; translated in Theor. Math. Phys., 1988, 76, 3, 895–903.
V. V. Borzov, E. V. Damaskinskiy, “Realization by a differential operator of the annihilation operator for generalized Chebyshev oscillator”, Zap. Nauchn. Sem. POMI, 494 (2020), 75–102
2.
V. V. Borzov, E. V. Damaskinskiy, “Calculating the Mandel parameter for an oscillator-like system generated by generalized Chebyshev polynomials”, Zap. Nauchn. Sem. POMI, 493 (2020), 73–87
2019
3.
V. V. Borzov, E. V. Damaskinsky, “Local perturbation of the discrete Schrödinger operator and a generalized Chebyshev oscillator”, TMF, 200:3 (2019), 494–506; Theoret. and Math. Phys., 200:3 (2019), 1348–1359
V. V. Borzov, E. V. Damaskinsky, “Invariance of the generalized oscillator under a linear transformation of the related system of orthogonal polynomials”, TMF, 190:2 (2017), 267–276; Theoret. and Math. Phys., 190:2 (2017), 228–236
V. V. Borzov, E. V. Damaskinsky, “Orthogonal polynomials and deformed oscillators”, TMF, 185:1 (2015), 68–76; Theoret. and Math. Phys., 185:1 (2015), 1417–1424
V. V. Borzov, E. V. Damaskinsky, “The discrete spectrum of Jacobi matrix related to recurrence relations with periodic coefficients”, Zap. Nauchn. Sem. POMI, 433 (2015), 111–130; J. Math. Sci. (N. Y.), 213:5 (2016), 694–705
2013
7.
V. V. Borzov, E. V. Damaskinsky, “Chebyshev–Koornwinder oscillator”, TMF, 175:3 (2013), 379–387; Theoret. and Math. Phys., 175:3 (2013), 763–770
V. V. Borzov, E. V. Damaskinsky, “Differential equations for the elementary 3-symmetric Chebyshev polynomials”, Zap. Nauchn. Sem. POMI, 398 (2012), 64–86; J. Math. Sci. (N. Y.), 192:1 (2013), 37–49
V. V. Borzov, E. V. Damaskinsky, “$N$-symmetric Chebyshev polynomials in a composite model of a generalized oscillator”, TMF, 169:2 (2011), 229–240; Theoret. and Math. Phys., 169:2 (2011), 1561–1572
V. V. Borzov, E. V. Damaskinsky, “Composite model for generalized oscillator. I”, Zap. Nauchn. Sem. POMI, 374 (2010), 58–81; J. Math. Sci. (N. Y.), 168:6 (2010), 789–804
V. V. Borzov, E. V. Damaskinsky, “Generalized coherent states for oscillators associated with the Charlier
$q$-polynomials”, TMF, 155:1 (2008), 39–46; Theoret. and Math. Phys., 155:1 (2008), 536–543
V. V. Borzov, E. V. Damaskinsky, “Coherent states for generalized oscillator in finite-dimensional Hilbert space”, Zap. Nauchn. Sem. POMI, 335 (2006), 75–99; J. Math. Sci. (N. Y.), 143:1 (2007), 2738–2753
V. V. Borzov, E. V. Damaskinsky, “Generalized coherent states for oscillators connected with Meixner and Meixner–Pollachek polynomials”, Zap. Nauchn. Sem. POMI, 317 (2004), 66–93; J. Math. Sci. (N. Y.), 136:1 (2006), 3564–3579
V. V. Borzov, E. V. Damaskinsky, “Generalized coherent states for $q$-oscillator connected with discrete $q$-Hermite polynomials”, Zap. Nauchn. Sem. POMI, 308 (2004), 48–66; J. Math. Sci. (N. Y.), 132:1 (2006), 26–36
V. V. Borzov, E. V. Damaskinsky, “Generalized coherent states: a novel approach”, Zap. Nauchn. Sem. POMI, 300 (2003), 65–71; J. Math. Sci. (N. Y.), 128:2 (2005), 2711–2715
V. V. Borzov, E. V. Damaskinsky, “Barut–Girardello Coherent states for the Gegenbauer oscillator”, Zap. Nauchn. Sem. POMI, 291 (2002), 43–63; J. Math. Sci. (N. Y.), 125:2 (2005), 123–135
V. V. Borzov, E. V. Damaskinsky, “Coherent states for the Legendre oscillator”, Zap. Nauchn. Sem. POMI, 285 (2002), 39–52; J. Math. Sci. (N. Y.), 122:5 (2004), 3473–3481
V. V. Borzov, E. V. Damaskinsky, S. B. Egorov, “Representations of the deformed oscillator algebra under different choices of generators”, Zap. Nauchn. Sem. POMI, 245 (1997), 80–106; J. Math. Sci. (New York), 100:2 (2000), 2061–2076
V. V. Borsov, “On the asymptotic behaviour of the Gauss functional integral”, Zap. Nauchn. Sem. LOMI, 184 (1990), 26–36; J. Math. Sci., 68:4 (1994), 411–418
V. V. Borzov, “High-temperature behavior of the partition function for the $P(\varphi)_2$ model of Euclidean field theory”, TMF, 76:3 (1988), 328–338; Theoret. and Math. Phys., 76:3 (1988), 895–903
1983
22.
V. V. Borzov, “Upper bound for the partition function of $P(\varphi)_2$ Euclidean field theory with Dirichlet boundary conditions”, TMF, 57:3 (1983), 373–381; Theoret. and Math. Phys., 57:3 (1983), 1203–1209
V. V. Borzov, “Asymptotic distribution of eigenvalues of secondarily quantized operator”, Mat. Zametki, 26:4 (1979), 547–560; Math. Notes, 26:4 (1979), 763–770
V. V. Borzov, “The spectrum of a singular string”, Izv. Vyssh. Uchebn. Zaved. Mat., 1976, no. 7, 3–10; Soviet Math. (Iz. VUZ), 20:7 (1976), 1–7
1973
25.
V. V. Borzov, “Piecewise polynomial approximations of functions of classes $\mathring W_p^r$ in $L_q$ with respect to an infinite measure”, Izv. Vyssh. Uchebn. Zaved. Mat., 1973, no. 8, 19–28
1971
26.
V. V. Borzov, “Certain applications of piecewise polynomial approximations of functions in the anisotropic classes $W_p^r$”, Dokl. Akad. Nauk SSSR, 198:3 (1971), 499–501
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