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

Keywords

43A55

Information

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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