01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
18.05.1955
Keywords:
differential inequalities; Green functions; elliptic functions; Chebyshev approximation; continued fractions; quadratic irrationalities
Subject:
Let $L$ be an elliptic differential operator of order $l>n/2$ in $R^n$. Let $\Omega\subset R^n$ be a bounded domain with Lipshitz boundary. The estimate $$-AG(x,x)^{1/2}G(y,y)^{1/2}\le G(x,y), x,y\in\Omega,$$ where $A
V. A. Malyshev, “A theorem on intersection with the $k$-dimensional barycenter”, Algebra i Analiz, 17:4 (2005), 115–124; St. Petersburg Math. J., 17:4 (2006), 635–640
2003
3.
V. A. Malyshev, “Periods of quadratic irrationalities, and torson of elliptic curves”, Algebra i Analiz, 15:4 (2003), 177–203; St. Petersburg Math. J., 15:4 (2004), 587–602
V. A. Malyshev, “Cell structure of the space of real polynomials”, Algebra i Analiz, 15:2 (2003), 40–127; St. Petersburg Math. J., 15:2 (2004), 191–248
V. A. Malyshev, “Estimates of the derivatives of $n$-convex functions”, Zap. Nauchn. Sem. POMI, 232 (1996), 123–133; J. Math. Sci. (New York), 92:1 (1998), 3622–3629
V. A. Malyshev, “The Bergman kernel and the Green function”, Zap. Nauchn. Sem. POMI, 221 (1995), 145–166; J. Math. Sci. (New York), 87:2 (1997), 3366–3380
V. A. Malyshev, “The Hadamard conjecture and estimates for the Green function”, Algebra i Analiz, 4:4 (1992), 1–44; St. Petersburg Math. J., 4:4 (1993), 633–666
V. A. Malyshev, “Differential inequalities and the Hadamard conjecture”, Dokl. Akad. Nauk, 323:3 (1992), 420–422; Dokl. Math., 45:2 (1992), 371–374
1991
12.
V. A. Malyshev, “Differential inequalities: embedding theorems and approximation
problems”, Dokl. Akad. Nauk SSSR, 319:3 (1991), 550–553; Dokl. Math., 44:1 (1992), 153–156
1988
13.
V. A. Malyshev, “Operators of differentiation and of increasing difference”, Izv. Vyssh. Uchebn. Zaved. Mat., 1988, no. 2, 49–50; Soviet Math. (Iz. VUZ), 32:2 (1988), 68–70
1985
14.
V. A. Malyshev, “Splines with a uniform step on the interval $[0,\infty)$”, Izv. Vyssh. Uchebn. Zaved. Mat., 1985, no. 12, 27–28; Soviet Math. (Iz. VUZ), 29:12 (1985), 35–37
1981
15.
V. A. Malyshev, A. V. Timofeev, “Dynamics of manipulators and adaptive control”, Avtomat. i Telemekh., 1981, no. 8, 90–98; Autom. Remote Control, 42:8 (1981), 1069–1076
Presentations in Math-Net.Ru
1.
Integrals with quadratic irrationalities V. A. Malyshev General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences December 11, 2003
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