A representation theorem for convolution transform with determining function in Lp

Chaim Danon; Dany Leviatan

doi:10.2140/pjm.1976.62.81

A representation theorem for convolution transform with determining function in L^p

Chaim Danon, Dany Leviatan

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Let G(t) be a kernel in Class II. Necessary conditions in order that a function f(x) be the convolution transform of ø(t)∈ L^p(−∞, ∞) were obtained by the second author. Also it was conjectured that the conditions are in fact sufficient. The conjecture is indeed true and we prove it here.

Original language	English
Pages (from-to)	81-86
Number of pages	6
Journal	Pacific Journal of Mathematics
Volume	62
Issue number	1
DOIs	https://doi.org/10.2140/pjm.1976.62.81
State	Published - Jan 1976

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abstract = "Let G(t) be a kernel in Class II. Necessary conditions in order that a function f(x) be the convolution transform of {\o}(t)∈ Lp(−∞, ∞) were obtained by the second author. Also it was conjectured that the conditions are in fact sufficient. The conjecture is indeed true and we prove it here.",

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A representation theorem for convolution transform with determining function in L^p

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