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Itogi Nauki i Tekhniki. Seriya "Matematicheskii Analiz", 1990, Volume 28, Pages 87–202
(Mi intm86)
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This article is cited in 45 scientific papers (total in 45 papers)
Operator semigroups, cosine operator functions, and linear differential equations
V. V. Vasil'ev, S. G. Krein, S. I. Piskarev
Abstract:
This survey presents a systematic exposition of the elements of the theory of operator semigroups (OS's) in Banach space from Hille–Yosida to the end of 1989. There is a parallel exposition of the theory of cosine operator functions (COF's). The paper contains the following divisions: Linear differential equations in Banach space, reduction of the Cauchy problem for second order equations to the Cauchy problem for first order equations, one-parameter OS's and COF's. differentiable OS's. analytic OS's. Fredholm OS's. positive OS's. stable OS's. spectral properties of OS's and COF's. compactness properties of OS's and COF's. uniformly continuous OS's and COF's. almost periodic OS's and COF's. uniformly bounded OS's and COF's. the theory of perturbations for OS's and COF's. ad joint OS's and COF's.
Citation:
V. V. Vasil'ev, S. G. Krein, S. I. Piskarev, “Operator semigroups, cosine operator functions, and linear differential equations”, Itogi Nauki i Tekhn. Ser. Mat. Anal., 28, VINITI, Moscow, 1990, 87–202; J. Soviet Math., 54:4 (1991), 1042–1129
Linking options:
https://www.mathnet.ru/eng/intm86 https://www.mathnet.ru/eng/intm/v28/p87
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