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The Conjugate Function on the Finite Dimensional Torus

Published online by Cambridge University Press:  20 November 2018

Nakhle Asmar
Nakhle Asmar*
Affiliation:
Department of Mathematics and Computer Science, California State University, Long Beach, Long Beach, California 90840
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Abstract

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We consider the group Ta, its group of characters Za, and an arbitrary order P on Za. For x ∊ Za, let sgnpx be 1, - 1 , or 0 according as x € P\{0}, x € (-P)\{0}, or X = 0. For f in Lp(Ta), 1 < p < ∞, it is known that there is a function in Lp(Ta) such that for all X in Za. Summability methods for are also available. In this paper, we obtain summability methods for that apply for in L1(Ta), and we show how various properties of can be derived from our construction.

Keywords

43A55
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 2 , 01 June 1989 , pp. 140 - 148
Copyright
Copyright © Canadian Mathematical Society 1989

References

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