The Fourier transform of bivariate functions that depend only on the maximum of the absolute values of their variables
Given an -function , necessary conditions and sufficient conditions for its Fourier transform to lie in and for the function to be in are indicated. The problem of the positivity of on is shown to be completely reducible to the same problem for the function in . Bibliography: 20 titles.
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| Veröffentlicht in: | Sbornik. Mathematics 2018-05, Vol.209 (5), p.759-779 |
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| container_title | Sbornik. Mathematics |
| container_volume | 209 |
| creator | Trigub, R. M. |
| description | Given an -function , necessary conditions and sufficient conditions for its Fourier transform to lie in and for the function to be in are indicated. The problem of the positivity of on is shown to be completely reducible to the same problem for the function in . Bibliography: 20 titles. |
| doi_str_mv | 10.1070/SM8888 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 1064-5616 |
| ispartof | Sbornik. Mathematics, 2018-05, Vol.209 (5), p.759-779 |
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| language | eng |
| recordid | cdi_iop_journals_10_1070_SM8888 |
| source | IOP Publishing Journals; Alma/SFX Local Collection |
| subjects | Bernstein's theorem on completely monotone functions Bivariate analysis Fourier transforms Lebesgue points Marcinkiewicz sums of a double Fourier series Mathematical analysis positive definiteness Wiener approximation theorem Wiener Banach algebra |
| title | The Fourier transform of bivariate functions that depend only on the maximum of the absolute values of their variables |
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