Eigenfunctions of the Cosine and Sine Transforms
A description of the eigensubspaces of the cosine and sine operators is given. The spectrum of each of these two operators consists of two eigen- values 1, -1 and their eigensubspaces are infinite{dimensional. There are many possible bases for these subspaces, but most popular are the ones construct...
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| Datum: | 2013 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2013
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| Schriftenreihe: | Журнал математической физики, анализа, геометрии |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/106768 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Eigenfunctions of the Cosine and Sine Transforms / V. Katsnelson // Журнал математической физики, анализа, геометрии. — 2013. — Т. 9, № 4. — С. 476-495. — Бібліогр.: 7 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | A description of the eigensubspaces of the cosine and sine operators is given. The spectrum of each of these two operators consists of two eigen- values 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 orthogo- nal 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)). |
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