A. M. Gomilko, “On the Inverse of the Generator of a Bounded $C_0$-Semigroup”, Funktsional. Anal. i Prilozhen., 38:4 (2004), 6–12; Funct. Anal. Appl., 38:4 (2004), 243

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Funktsional'nyi Analiz i ego Prilozheniya, 2004, Volume 38, Issue 4, Pages 6–12
DOI: https://doi.org/10.4213/faa122 (Mi faa122)

This article is cited in 7 scientific papers (total in 7 papers)

On the Inverse of the Generator of a Bounded $C_0$-Semigroup

A. M. Gomilko

Institute of Hydromechanics of NAS of Ukraine

Full-text PDF (153 kB) Citations (7)

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DOI: https://doi.org/10.4213/faa122

Abstract: Let $A$ be the generator of a uniformly bounded $C_0$-semigroup in a Banach space $B$, and let $A$ have a densely defined inverse $A^{-1}$. We present sufficient conditions on the resolvent $(A-\lambda I)^{-1}$, $\operatorname{Re}\lambda>0$, under which $A^{-1}$ is also the generator of a uniformly bounded $C_0$-semigroup.

Keywords: uniformly bounded $C_0$-semigroup, inverse of the generator, Banach space, Carleson embedding theorem.

Received: 11.08.2003

English version:
Functional Analysis and Its Applications, 2004, Volume 38, Issue 4, Pages 243–248
DOI: https://doi.org/10.1007/s10688-005-0002-z

Bibliographic databases:

Document Type: Article

UDC: 517.9

Language: Russian

Citation: A. M. Gomilko, “On the Inverse of the Generator of a Bounded $C_0$-Semigroup”, Funktsional. Anal. i Prilozhen., 38:4 (2004), 6–12; Funct. Anal. Appl., 38:4 (2004), 243–248

Citation in format AMSBIB

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https://doi.org/10.4213/faa122

https://www.mathnet.ru/eng/faa/v38/i4/p6

This publication is cited in the following 7 articles:

Li M., Pastor J., Piskarev S., “Inverses of Generators of Integrated Fractional Resolvent Operator Functions”, Fract. Calc. Appl. Anal., 21:6 (2018), 1542–1564
deLaubenfels R., “Inverses of generators of nonanalytic semigroups”, Studia Math., 191:1 (2009), 11–38
A. M. Gomilko, H. Zwart, Yu. Tomilov, “Inverse operator of the generator of a $C_0$-semigroup”, Sb. Math., 198:8 (2007), 1095–1110
Zwart H., “Growth estimates for $\exp(A^{-1}t)$ on a Hilbert space”, Semigroup Forum, 74:3 (2007), 487–494
Gomilko A., Zwart H., “The Cayley transform of the generator of a bounded $C_0$-semigroup”, Semigroup Forum, 74:1 (2007), 140–148
deLaubenfels R., “Inverses of generators of integrated or regularized semigroups”, Semigroup Forum, 75:2 (2007), 457–463
Zwart H., “Is A(-1) an infinitesimal generator?”, Perspectives in Operator Theory, Banach Center Publications, 75, 2007, 303–313

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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References:	81

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