Functional Equations and Weierstrass Transforms |
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Authors: | John A Baker |
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Institution: | 1. Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
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Abstract: | The purpose of this article is to illustrate the utility of the Weierstrass transform in the study of functional equations (and systems) of the form 1 $${\mathop \sum^N\limits_{k=0}}\alpha_{k}f(x+r_{k})=f_{0}(x)\ \ \ \, x\in\ {\rm R}.$$ One may think of α0, α1,…, αN as given complex numbers, r0, r1,…, rN as given real numbers, ?0: ? → C as a given function and ? as the unknown. |
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