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Журнал математической физики, анализа, геометрии, 2013, том 9, номер 4, страницы 476–495
(Mi jmag577)
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Eigenfunctions of the Cosine and Sine Transforms
V. Katsnelson The Weizmann Institute of Science,
Rehovot 76100, Israel
Аннотация:
A description of the eigensubspaces of the cosine and sine operators is given. The spectrum of each of these two operators consists of two eigenvalues $(1,-1)$ and their eigensubspaces are infinite-dimensional. There are many possible bases for these subspaces, but most popular are the ones constructed from the Hermite functions. We present other "bases" which are not discrete orthogonal sequences of vectors, but continuous orthogonal chains of vectors. Our work can be considered to be a continuation and further development of the results obtained by Hardy and Titchmarsh: “Self-reciprocal functions” (Quart. J. Math., Oxford, Ser. 1 (1930)).
Ключевые слова и фразы:
Fourier transform, cosine-sine transforms, eigenfunctions, Melline transform.
Поступила в редакцию: 29.10.2012 Исправленный вариант: 17.12.2012
Образец цитирования:
V. Katsnelson, “Eigenfunctions of the Cosine and Sine Transforms”, Журн. матем. физ., анал., геом., 9:4 (2013), 476–495
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag577 https://www.mathnet.ru/rus/jmag/v9/i4/p476
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Страница аннотации: | 184 | PDF полного текста: | 79 | Список литературы: | 47 |
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