Uniqueness of Gabor series
نویسندگان
چکیده
منابع مشابه
Uniqueness of Representation by Trigonometric Series
In 1870 Georg Cantor proved that a 2s periodic complex valued function of a real variable coincides with the values of at most one trigonometric series. We present his proof and then survey some of the many one dimensional generalizations and extensions of Cantor's theorem. We also survey the situation in higher dimensions, where a great deal less is known. 1. Cantor's uniqueness theorem. In 18...
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In 1870 Georg Cantor proved that a 2sr periodic omplex valued function of a real variable coincides with the values of at most one trigonometric series. We present his proof and then survey some of the many one dimensional generalizations and extensions of Cantor's theorem. We also survey the situation in higher dimensions, where a great deal less is known. 1. Cantor's uniqueness theorem. In 18...
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We survey some recent results on the uniqueness questions on multiple trigonometric series. Two basic questions, one about series which converges to zero and the other about the series which converge to an integrable function, are asked for four modes of convergence: unrestricted rectangular convergence, spherical convergence, square convergence, and restricted rectangular convergence. We will ...
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Five uniqueness questions for multiple trigonometric series are surveyed. If a multiple trigonometric series converges everywhere to zero in the sense of spherical convergence, of unrestricted rectangular convergence, or of iterated convergence, then that series must have every coefficient being zero. But the cases of square convergence and restricted rectangular convergence lead to open questi...
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A uniqueness theorem is proved for trigonometric series and another one is proved for multiple trigonometric series. A corollary of the second theorem asserts that there are two subsets of the d-dimensional torus, the first having a countable number of points and the second having 2d points such that whenever a multiple trigonometric series "converges" to zero at each point of the former set an...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2015
ISSN: 1063-5203
DOI: 10.1016/j.acha.2015.03.006