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This article is cited in 1 scientific paper (total in 1 paper)
Research Papers
Spectrally reasonable measures
P. Ohrysko, M. Wojciechowski Institute of Mathematics, Polish Academy of Sciences,00-956 Warszawa, Poland
Abstract:
The problems under study are related to measures with a natural spectrum (equal to the closure of the set of the values of the Fourier–Stieltjes transform). Since it is known that the set of all such measures does not have a Banach algebra structure, the set of all suitable perturbations called spectrally reasonable measures is considered. In particular, a broad class of spectrally reasonable measures is exhibited, which contains absolutely continuous ones. On the other hand, it is shown that except trivial cases all discrete (purely atomic) measures do not posses this property.
Keywords:
natural spectrum, Wiener–Pitt phenomenon, Fourier–Stieltjes coefficients, convolution algebra, spectrum of measure.
Received: 25.11.2015
Citation:
P. Ohrysko, M. Wojciechowski, “Spectrally reasonable measures”, Algebra i Analiz, 28:2 (2016), 187–203; St. Petersburg Math. J., 28:2 (2017), 259–271
Linking options:
https://www.mathnet.ru/eng/aa1490 https://www.mathnet.ru/eng/aa/v28/i2/p187
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Abstract page: | 189 | Full-text PDF : | 41 | References: | 28 | First page: | 10 |
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