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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Bibliographische Detailangaben
Veröffentlicht in:	Sbornik. Mathematics 2018-05, Vol.209 (5), p.759-779
1. Verfasser:	Trigub, R. M.
Format:	Artikel
Sprache:	eng
Schlagworte:	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
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Beschreibung
Zusammenfassung:	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.
ISSN:	1064-5616 1468-4802
DOI:	10.1070/SM8888