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Spectrally reasonable measures


Authors: P. Ohrysko and M. Wojciechowski
Original publication: Algebra i Analiz, tom 28 (2016), nomer 2.
Journal: St. Petersburg Math. J. 28 (2017), 259-271
MSC (2010): Primary 43A10
DOI: https://doi.org/10.1090/spmj/1449
Published electronically: February 15, 2017
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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 the absolutely continuous ones. On the other hand, it is shown that except trivial cases all discrete (purely atomic) measures do not possess this property.


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Additional Information

P. Ohrysko
Affiliation: Institute of Mathematics, Polish Academy of Sciences, 00-956 Warszawa, Poland
Email: p.ohrysko@gmail.com

M. Wojciechowski
Affiliation: Institute of Mathematics, Polish Academy of Sciences, 00-956 Warszawa, Poland
Email: miwoj-impan@o2.pl

DOI: https://doi.org/10.1090/spmj/1449
Keywords: Natural spectrum, Wiener--Pitt phenomenon, Fourier--Stieltjes coefficients, convolution algebra, spectrum of measure
Received by editor(s): November 25, 2015
Published electronically: February 15, 2017
Additional Notes: The research of the first author was supported by National Science Centre, Poland, grant no. 2014/15/N/ST1/02124
Article copyright: © Copyright 2017 American Mathematical Society