This article is cited in 2 papers

The Gearhart–Prüss Theorem for a Class of Degenerate Semigroups of Operators

A. G. Chshiev

Voronezh State University

Abstract: We consider a class of semigroups of operators in Hilbert space whose generators are linear relations. An analog of the Gearhart–Prüss theorem for semigroups of operators from the class under consideration is obtained.

Keywords: semigroups of operators in Hilbert space, Gearhart–Prüss theorem, linear relation, complex Hilbert space, infinitesimal operator, exponential dichotomy.

UDC: 517.9

Received: 24.05.2011
Revised: 25.10.2011

DOI: 10.4213/mzm9174

 English version: Mathematical Notes, 2013, 94:3, 400–413

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