Abstract
We consider generators of certain operator semigroups and study the closeness and closability properties of certain generators (in the operator class). We obtain the necessary and sufficient conditions for these properties.
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E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups (Providence, Amer. Math. Soc., 1957; Inost. Lit.,Moscow, 1962).
A.G. Baskakov, “Linear Relations as Generators of Operator Semigroups,” Matem. Zametki 84(2), 175–192 (2008).
A. G. Baskakov and K. I. Chernyshev, “Spectral Analysis of Linear Relations and Degenerate Operator Semigroups,” Matem. Sborn. 193(11), 3–42 (2002).
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Original Russian Text © A.G. Chshiev, 2011, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, No. 8, pp. 77–85.
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Chshiev, A.G. The closeness and closability criteria for infinitesimal operators of certain semigroups. Russ Math. 55, 66–74 (2011). https://doi.org/10.3103/S1066369X1108010X
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DOI: https://doi.org/10.3103/S1066369X1108010X