The Weierstrass transform is examined on the space of Lebesgue measurable function on Rn having at most exponential growth, thereby extending to higher dimensions the one-dimensional consideration of . The resulting theory has utility in the study of certain functional equations of “translation” type; two such applications are presented.
1991 Mathematics Subject Classification
39B99 44A15 39A99
Functional equations Weierstrass transform
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S. Haruki and C.T. Ng, Partial difference equations analogous to the Cauchy-Riemann equations and related functional equations on rings and fields, Results in Mathematics, 26 (1994), 316–323.MathSciNetMATHCrossRefGoogle Scholar