Abstract
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 [4]. The resulting theory has utility in the study of certain functional equations of “translation” type; two such applications are presented.
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References
J. Aczél, Lectures on Functional Equations and Their Applications. Academic Press, New York-London, 1966.
J. Aczél and S. Haruki, Partial differential equations analogous to the Cauchy-Riemann equations, Funkcial. Ekvac. 24 (1981), 95–102.
John A. Baker, Functional Equations, Distribution and Approximate Identities, Canad. J. Math. 42 (1990), 696–708.
John A. Baker, Functional Equations and Weierstrass Transforms, Results in Mathematics, 26 (1994), 199–204.
John A. Baker, Some propositions related to a dilation theorem of W. Benz, Aequationes Math. 47 (1994), 79–88.
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.
R. Narasimhan, Complex Analysis in One Variable, Birkhäuser, Boston, 1985.
A.H. Zemanian, Generalized Integral Transformations, Dover, New York, 1968.
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Baker, J.A. Functional Equations and Weierstrass Transforms II. Results. Math. 31, 282–291 (1997). https://doi.org/10.1007/BF03322165
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DOI: https://doi.org/10.1007/BF03322165