On a characterization of compactness and the Abel-Poisson summability of fourier coefficients in Banach spaces
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In this paper, for an isometric strongly continuous linear representation denoted by ? of the topological group of the unit circle in complex Banach space, we study an integral representation for Abel-Poisson mean A?r (x) of the Fourier coefficients family of an element x, and it is proved that this family is Abel-Poisson summable to x. Finally, we give some tests which are related to characterizations of relatively compactness of a subset by means of Abel-Poisson operator A?r and ?.
1957 ◽
Vol 53
(3)
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pp. 576-580
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2019 ◽
Vol 38
(3)
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pp. 133-140
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2002 ◽
Vol 54
(6)
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pp. 1165-1186
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1983 ◽
Vol 26
(2)
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pp. 163-167
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1995 ◽
Vol 58
(2)
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pp. 222-231
1974 ◽
Vol 76
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pp. 157-159
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2020 ◽
Vol 1664
(1)
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pp. 012038