Abstract
We establish conditions for the behavior of the resolvent and the location of the spectrum of a linear closed operator A densely defined in a Banach space E under which its Gevrey spaces G (β)(A), β < 1, are dense in E.
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REFERENCES
E. Nelson, “Analytic vectors,” Ann. Math., (2)70, No. 3, 572–615 (1959).
R. Goodman, “Analytic and entire vectors for representations of Lie groups,” Trans. Amer. Math. Soc., 143, 55–76 (1969).
Ya. V. Radyno, “Space of vectors of exponential type,” Dokl. Akad. Nauk Belorus. SSR, 27, No.9, 791–793 (1983).
I. M. Gel'fand, “On one-parameter groups of operators in a normed space,” Dokl. Akad. Nauk SSSR, 25, No.9, 713–718 (1939).
A. V. Knyazyuk, Boundary Values of Infinitely-Differentiable Semigroups [in Russian], Preprint No. 69, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1985).
Yu. M. Berezanskii, G. F. Us, and Z. G. Sheftel', Functional Analysis [in Russian], Vyshcha Shkola, Kiev (1990).
R. Beals, “Semigroups and abstract Gevrey spaces,” J. Funct. Anal., 10, No.3, 300–308 (1972).
I. M. Gel'fand and G. E. Shilov, Spaces of Test and Generalized Functions [in Russian], Fizmatgiz, Moscow (1958).
H. B. Dwight, Tables of Integrals and Other Mathematical Data [Russian translation], Inostrannaya Literatura, Moscow (1948).
V. I. Gorbachuk and A. V. Knyazyuk, “Boundary values of solutions of operator-differential equations,” Usp. Mat. Nauk, 44, No.3, 55–91 (1989).
D. Fujiwara, “A characterization of exponential distribution of semigroups,” J. Math. Soc. Jpn., 18, No.3, 267–274 (1966).
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Mokrousov, Y.G. On the Denseness of Subspaces of Analytic Vectors of a Closed Linear Operator in a Banach Space. Ukrainian Mathematical Journal 52, 1130–1133 (2000). https://doi.org/10.1023/A:1005242103529
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DOI: https://doi.org/10.1023/A:1005242103529