Logarithmic Capacity of Sets and Double Trigonometric Series

Author:

Shapiro V. L.

Abstract

It is the purpose of this paper to establish a closer connection between the logarithmic capacity of sets and double trigonometric series. In (9), closed sets of logarithmic capacity zero were established as sets of uniqueness for a particular class of double trigonometric series under circular (C, 1) summability. By slightly changing this class of series but still maintaining closed sets of logarithmic capacity zero as sets of uniqueness, it is shown in this paper that closed sets of positive logarithmic capacity form sets of multiplicity.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Multiple fourier series and integrals;Journal of Soviet Mathematics;1984-03

2. Fourier-Laplace series on a sphere;Journal of Soviet Mathematics;1979-12

3. Fourier series in several variables;Bulletin of the American Mathematical Society;1964

4. Generalized Laplacians;American Journal of Mathematics;1956-07

5. Laplace series and sets of logarithmic capacity zero;Proceedings of the American Mathematical Society;1955

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