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Logarithmic Capacity of Sets and Double Trigonometric Series

Published online by Cambridge University Press:  20 November 2018

V. L. Shapiro
V. L. Shapiro*
Affiliation:
Rutgers University and The Institute for Advanced Study
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 582 - 592
Copyright
Copyright © Canadian Mathematical Society 1954

References

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