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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

To the theory of infinitely differentiable semigroups of operators


Author: M. S. Bichegkuev
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 22 (2010), nomer 2.
Journal: St. Petersburg Math. J. 22 (2011), 175-182
MSC (2010): Primary 47A56
Published electronically: February 8, 2011
MathSciNet review: 2668123
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Abstract | References | Similar Articles | Additional Information

Abstract: Given a linear relation (multivalued linear operator) with certain growth restrictions on the resolvent, an infinitely differentiable semigroup of operators is constructed. It is shown that the initial linear relation is a generator of this semigroup. The results obtained are intimately related to certain results in the monograph "Functional analysis and semi-groups'' by Hille and Phillips.


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Additional Information

M. S. Bichegkuev
Affiliation: K. Khetagurov North Osetian State University, 46 Vatutina Street, Vladikavkaz 362025, RSO-Alaniya, Russia
Email: bichegkuev@yandex.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2011-01137-9
PII: S 1061-0022(2011)01137-9
Keywords: Linear relation, infinitely differentiable semigroup of operators, generator of a semigroup, resolvent set
Received by editor(s): April 6, 2009
Published electronically: February 8, 2011
Additional Notes: Supported by RFBR (grant no. 07-01-00131)
Article copyright: © Copyright 2011 American Mathematical Society