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: 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.

References [Enhancements On Off] (What's this?)

  • 1. Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. MR 0089373
  • 2. Angelo Favini and Atsushi Yagi, Degenerate differential equations in Banach spaces, Monographs and Textbooks in Pure and Applied Mathematics, vol. 215, Marcel Dekker, Inc., New York, 1999. MR 1654663
  • 3. Ronald Cross, Multivalued linear operators, Monographs and Textbooks in Pure and Applied Mathematics, vol. 213, Marcel Dekker, Inc., New York, 1998. MR 1631548
  • 4. A. G. Baskakov, Linear relations as generators of semigroups of operators, Mat. Zametki 84 (2008), no. 2, 175–192 (Russian, with Russian summary); English transl., Math. Notes 84 (2008), no. 1-2, 166–183. MR 2475046, 10.1134/S0001434608070183
  • 5. A. G. Baskakov, Theory of representations of Banach algebras, and abelian groups and semigroups in the spectral analysis of linear operators, Sovrem. Mat. Fundam. Napravl. 9 (2004), 3–151 (electronic) (Russian); English transl., J. Math. Sci. (N. Y.) 137 (2006), no. 4, 4885–5036. MR 2123307, 10.1007/s10958-006-0286-4
  • 6. A. G. Baskakov and K. I. Chernyshov, Spectral analysis of linear relations, and degenerate semigroups of operators, Mat. Sb. 193 (2002), no. 11, 3–42 (Russian, with Russian summary); English transl., Sb. Math. 193 (2002), no. 11-12, 1573–1610. MR 1937028, 10.1070/SM2002v193n11ABEH000696
  • 7. S. G. Kreĭn, Lineikhye differentsialnye uravneniya v Banakhovom prostranstve, Izdat. “Nauka”, Moscow, 1967 (Russian). MR 0247239
    S. G. Kreĭn, Linear differential equations in Banach space, American Mathematical Society, Providence, R.I., 1971. Translated from the Russian by J. M. Danskin; Translations of Mathematical Monographs, Vol. 29. MR 0342804
  • 8. M. S. Bichegkuev, On a weakened Cauchy problem for a linear differential inclusion, Mat. Zametki 79 (2006), no. 4, 483–487 (Russian, with Russian summary); English transl., Math. Notes 79 (2006), no. 3-4, 449–453. MR 2251138, 10.1007/s11006-006-0051-5

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Additional Information

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

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