Spectrally reasonable measures
| Autor: | Przemysław Ohrysko, Michał Wojciechowski |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Class (set theory)
Pure mathematics Algebra and Number Theory Property (philosophy) Applied Mathematics 010102 general mathematics Spectrum (functional analysis) Structure (category theory) Absolute continuity 01 natural sciences Functional Analysis (math.FA) Mathematics - Functional Analysis 010101 applied mathematics Set (abstract data type) Closure (mathematics) Banach algebra FOS: Mathematics 0101 mathematics Analysis Mathematics |
| Zdroj: | St. Petersburg Mathematical Journal. 28:259-271 |
| ISSN: | 1547-7371 1061-0022 |
| Popis: | In this paper we investigate the problems 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 we consider the set of all suitable perturbations called spectrally reasonable measures. In particular, we exhibit a broad class of spectrally reasonable measures which contains absolutely continuous ones. On the other hand, we show that except trivial cases all discrete (purely atomic) measures do not posses this property. St. Petersburg Mathematical Journal vol. 28 (2016) no. 2 |
| Databáze: | OpenAIRE |
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