This article is cited in 15 papers

Slowly varying on infinity semigroups of operators

A. G. Baskakov, N. S. Kaluzhina, D. M. Polyakov

Chair of Mathematical Methods of Operational Research, Voronezh State University, 1 Universitetskaya sq., Voronezh, 394006 Russia

Abstract: We study the asymptotical behavior of bounded semigroups of linear operators in Banach spaces. The results are tightly connected with research of stabilisation of solutions of parabolic equations when time tends to infinity. The traditional condition of existence of an average of initial functions is not required.

Keywords: slowly varying functions, semigroups of linear operators, Beurling spectrum, harmonic analysis.

UDC: 517.9

Received: 19.12.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:7, 1–10

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