Classes of entire functions that are rapidly decreasing on the real axis: theory and applicationsстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:Two types of classes of entire functions (W-alpha and Z(alpha)), which are rapidly decreasing on the real axis are considered. Conditions to ensure that these classes are non-trivial are found and the classes of the corresponding Fourier transforms are described. Results on the classes Z(alpha) are applied to the question of whether a rapidly decreasing function with rapidly decreasing Fourier transform is trivial. This yields not just an extension of Morgan's well-known theorem, but also its converse.