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• W35302616 abstract "We study the reduced Beurling spectra spA,V (F) of functions F 2 L 1(J,X) relative to certain function spaces AL 1 (J,X) and VL 1 (R), where J is R+ or R and X is a Banach space. We show that if F is bounded or slowly oscillat- ing on J with 0 㘲 spA,S(F), where A is f0g or C0(J,X) for example and S = S(R), then F is ergodic. This result is new even for F 2 BUC(J,X) and A = C0(J,X). If F is ergodic and belongs to the space S0 ar(J,X) of absolutely regular distributions and ifspC0(J,X),S(F) = ;, then F� 2 C0(R,X) for all 2 S (R). Here, FjJ = F and Fj(R n J) = 0. We show that tauberian theorems for Laplace transforms follow from results about the reduced spectrum. Our results are more widely applicable than those of previous authors. We demonstrate this and the sharpness of our results through examples" @default.
• W35302616 created "2016-06-24" @default.
• W35302616 creator A5040681947 @default.
• W35302616 creator A5060733841 @default.
• W35302616 date "2010-06-17" @default.
• W35302616 modified "2023-09-27" @default.
• W35302616 title "Spectral characterization of absolutely regular vector-valued distributions" @default.
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• W35302616 hasPublicationYear "2010" @default.
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