A problem of Wiener and the failure of a principle for Fourier series with positive coefficients

Stephen Wainger

Type: Article

Publication Date: 1969-01-01

Citations: 15

DOI: https://doi.org/10.1090/s0002-9939-1969-0236397-8

Abstract

Wiener proved the following theorem [l].Theorem A. Let 00 F(z) = S anzn n-0 be analytic in \z\ <1, and assume an = 0. Furthermore, assume for some 5>0, sup I | F(reie)\2d6 = M < ».

Locations

Proceedings of the American Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+	On Fourier series with non-negative coefficients and two problems of R. P. Boas	1985	Ling-Yau Chan
+	Concerning the Fourier Coefficients of a Nonnegative Function	1960	Gábor Szegő
+ PDF Chat	A Strong Converse of the Wiener-Levy Theorem	1962	Walter Rudin
+	The mathematics of Wiener’s Tauberian theorem	1997	Lars Gårding
+	A version of Wiener’s and Lévy’s theorems	2008	A. El Kinani
+	[60–2] Concerning the Fourier Coefficients of a Nonnegative Function	1982	G. Szegö
+ PDF Chat	An Abstract Wiener-Levy Theorem on Fourier Transforms	1973	Morisuke Hasumi Sin‐Ei Takahasi
+	On a problem of strong summability of Fourier series	1968	Л. Леиндлер
+	A Theorem Concerning Fourier Series	1923	Torsten Carleman
+ PDF Chat	Fourier series with positive coefficients	1967	R. P. Boas
+	A Faber-Krahn inequality with drift	2006	François Hamel Nikolaï Nadirashvili Emmanuel Russ
+ PDF Chat	A simple proof of Wiener’s $1/f$ theorem	1975	David Newman
+	Wiener's lemma	2013	Henrik Fredriksson
+	A Direct Proof of Wiener’s Theorem	2012	Matthew Hendtlass Schuster Peter
+	On a problem of Hardy for Walsh-Fourier series	2010	С. В. Бочкарев
+	An Inequality for the Fourier Coefficients of a Nonnegative Funtion	1959	J. D. Weston
+	A singularity of the Fourier series of continuous functions	1943	R. Salem
+	A Remark on the Study of Convergence of Fourier Series	1991	V. М. Tikhomirov
+	A Remark on Wiener's Tauberian Theorem	1965	M. Kac
+	Pointwise convergence in Pringsheim’s sense of the summability of Fourier transforms on Wiener amalgam spaces	2013	Ferenc Weisz

Works That Cite This (14)

Action	Title	Year	Authors
+	Wiener's theorem for positive definite functions on hypergroups	2014	Walter R. Bloom John J. F. Fournier Michael Leinert
+ PDF Chat	ON INTEGRAL ESTIMATES OF NONNEGATIVE POSITIVE DEFINITE FUNCTIONS	2017	А. В. Ефимов Marcell Gaál Szilárd Gy. Révész
+ PDF Chat	Failure of Wiener's property for positive definite periodic functions	2008	Aline Bonami Szilárd Gy. Révész
+ PDF Chat	Fourier decompositions with positive coefficients in compact Gel′fand pairs	1993	Brian E. Blank
+ PDF Chat	Wiener’s problem for positive definite functions	2017	Д. В. Горбачев Sergey Tikhonov
+ PDF Chat	Fourier series with positive coefficients	1987	J. Marshall Ash Michael Rains Stephen Vági
+ PDF Chat	Laguerre and Disk Polynomial Expansions with Nonnegative Coefficients	2013	Yūichi Kanjin
+	Solution of Integral of The Fourth Power of a Finite-Length Exponential Fourier Series	2023	Hesham Sharkas
+ PDF Chat	Integral comparisons of nonnegative positive definite functions on LCA groups	2022	Marcell Gaál Szilárd Gy. Révész
+	On integral estimates of non-negative positive definite functions	2016	А. В. Ефимов Marcell Gaál Szilárd Gy. Révész

Works Cited by This (2)

Action	Title	Year	Authors
+	Integrability theorems for trigonometric transforms	1967	R. P. Boas
+ PDF Chat	Fourier series with positive coefficients	1967	R. P. Boas