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- W2088144996 abstract "In this paper we shall study the problem of localization in the case of double trigonometric series summed by the method of circular summation introduced by Bochner in his treatment of multiple Fourier series [1 I(). To develop our theory of localization we shall use the process of formal multiplication of series in a manner analogous to that employed by Rajchman and Zygmund [6] in their investigations of localization phenomena exhibited by trigonometric series in one variable. However, we shall apply these ideas to circular sums and means. We also extend our results to higher dimensions and consider briefly types of summation defined by certain convex curves. The author would like to take this opportunity to thank Professor Antoni Zygmund for suggesting this problem and for his guidance and encouragement. 1. Definitions and notation. A double trigonometric series is a seriesof the form" @default.
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- W2088144996 date "1951-02-01" @default.
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- W2088144996 title "Circular summation and localization of double trigonometric series" @default.
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- W2088144996 doi "https://doi.org/10.1090/s0002-9947-1951-0040464-2" @default.
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