periodic Shrödinger operator, discrete spectrum in the gaps of the continuos one, Stark operator, Spectral Shift Function, large coupling constant.
UDC:
517.43
Subject:
Spectral theory of differential operators.
Main publications:
V. A. Sloushch, “Discrete spectrum appearing in the spectral gaps under the strong perturbations with definite sign”, Trudy Sankt-Peterburgskogo mat. obshchestva, 6, 1998, 213–230
V. A. Sloushch, “Discrete spectrum of the differential operators in the spectral gaps under non-negative perturbations of the high order”, Zapiski nauchnyh seminarov POMI, 270, 2000, 325–335
A. Pushnitski, V. Sloushch, “Spectral shift function for the Stark operator in the large coupling
constant limit”, Asymptot. Anal., 51:1 (2007), 63–89
V. A. Sloushch, “Some generalizations of the Cwikel estimate for the integral operators”, Trudy Sankt-Peterburgskogo mat. obshchestva, 14, 2008
V. A. Sloushch, T. A. Suslina, “Operator estimates for homogenization of higher-order elliptic operators with periodic coefficients”, Algebra i Analiz, 35:2 (2023), 107–173; St. Petersburg Math. J., 35:2 (2024), 327–375
A. A. Raev, V. A. Sloushch, T. A. Suslina, “Homogenization of a one-dimensional fourth-order periodic operator with a singular potential”, Zap. Nauchn. Sem. POMI, 521 (2023), 212–239
2022
3.
A. A. Mishulovich, V. A. Sloushch, T. A. Suslina, “Homogenization of a one-dimensional periodic elliptic operator at the edge of a spectral gap: operator estimates in the energy norm”, Zap. Nauchn. Sem. POMI, 519 (2022), 114–151
V. A. Sloushch, T. A. Suslina, “Threshold approximations for the resolvent of a polynomial nonnegative operator pencil”, Algebra i Analiz, 33:2 (2021), 233–274; St. Petersburg Math. J., 33:2 (2022), 355–385
E. L. Korotyaev, V. A. Sloushch, “Asymptotics and estimates for the discrete spectrum of the Schrödinger operator on a discrete periodic graph”, Algebra i Analiz, 32:1 (2020), 12–39; St. Petersburg Math. J., 32:1 (2021), 9–29
V. A. Sloushch, T. A. Suslina, “Homogenization of the Fourth-Order Elliptic Operator with Periodic Coefficients with Correctors Taken into Account”, Funktsional. Anal. i Prilozhen., 54:3 (2020), 94–99; Funct. Anal. Appl., 54:3 (2020), 224–228
V. A. Sloushch, “Cwikel type estimate for the sandwiched Airy transform”, Algebra i Analiz, 29:2 (2017), 127–138; St. Petersburg Math. J., 29:2 (2018), 315–323
2015
8.
V. A. Sloushch, “Discrete spectrum of the periodic Schrödinger operator with a variable metric perturbed by a nonnegative rapidly decaying potential”, Algebra i Analiz, 27:2 (2015), 196–210; St. Petersburg Math. J., 27:2 (2016), 317–326
V. A. Sloushch, “Approximate commutation of a decaying potential and a function of elliptic operator”, Algebra i Analiz, 26:5 (2014), 215–227; St. Petersburg Math. J., 26:5 (2015), 849–857
V. A. Sloushch, “Cwikel type estimates as a consequence of some properties of the heat kernel”, Algebra i Analiz, 25:5 (2013), 173–201; St. Petersburg Math. J., 25:5 (2014), 835–854
M. Sh. Birman, V. A. Sloushch, “Two-Sided Estimates for the Trace of the Difference of Two Semigroups”, Funktsional. Anal. i Prilozhen., 43:3 (2009), 26–32; Funct. Anal. Appl., 43:3 (2009), 184–189
V. A. Sloushch, “The discrete spectrum of differential operators in the spectral gaps in the case of nonnegative perturbations of
higher order”, Zap. Nauchn. Sem. POMI, 270 (2000), 325–335; J. Math. Sci. (N. Y.), 115:2 (2003), 2272–2278
13.
V. A. Sloushch, “The discrete spectrum asymptotics with large coupling constant in the case of strong nonnegative perturbations”, Zap. Nauchn. Sem. POMI, 270 (2000), 317–324; J. Math. Sci. (N. Y.), 115:2 (2003), 2267–2271
1997
14.
V. A. Sloushch, “Discrete spectrum in the spectral gaps of a selfadjoint operator for unbounded perturbations”, Zap. Nauchn. Sem. POMI, 247 (1997), 237–241; J. Math. Sci. (New York), 101:3 (2000), 3190–3192
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