Uniqueness of double Fourier-Stieltjes series

被引：0

作者：

Móricz, F ^{[1
]}

机构：

[1] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary

来源：

ARCHIV DER MATHEMATIK | 2002年 / 78卷 / 01期

关键词：

Borel Measure;

D O I：

10.1007/s00013-002-8216-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the double Fourier-Stieltjes series dF(x, y) of a function F of bounded variation over [0, 2pi] x [0, 2pi] in the sense of Hardy and Krause. We give necessary and sufficient conditions to ensure that dF vanishes identically. If, in addition, F is periodic in each variable, then the necessary and sufficient condition can be expressed in terms of the Borel measure induced by F.

引用

页码：51 / 57

页数：7

共 7 条

[1] Properties of functions f(x, y) of bounded variation
Adams, C. Raymond
Clarkson, James A.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1934, 36 (1-4) : 711 - 730
[2] On definitions of bounded variation for functions of two variables
Clarkson, James A.
Adams, C. Raymond
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1933, 35 (1-4) : 824 - 854
[3] Hardy GH., 1905, Q J MATH, V37, P53
[4] Hobson EW, 1927, The theory of functions of a real variable and the theory of fourier series, V1
[5] Extension of a theorem of Fejer to double Fourier-Stieltjes series
Móricz, F
[J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2001, 7 (06) : 601 - 614
[6] Riesz F., 1990, Functional Analysis
[7] ZYMUND A, 1959, TRIGONOMETRIC SERIES

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