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Results in Mathematics

, Volume 31, Issue 3–4, pp 282–291 | Cite as

Functional Equations and Weierstrass Transforms II

  • John A. Baker
Research article
  • 51 Downloads

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.

1991 Mathematics Subject Classification

39B99 44A15 39A99 

En]Keywords

Functional equations Weierstrass transform 

References

  1. 1.
    J. Aczél, Lectures on Functional Equations and Their Applications. Academic Press, New York-London, 1966.MATHGoogle Scholar
  2. 2.
    J. Aczél and S. Haruki, Partial differential equations analogous to the Cauchy-Riemann equations, Funkcial. Ekvac. 24 (1981), 95–102.MathSciNetMATHGoogle Scholar
  3. 3.
    John A. Baker, Functional Equations, Distribution and Approximate Identities, Canad. J. Math. 42 (1990), 696–708.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    John A. Baker, Functional Equations and Weierstrass Transforms, Results in Mathematics, 26 (1994), 199–204.MATHCrossRefGoogle Scholar
  5. 5.
    John A. Baker, Some propositions related to a dilation theorem of W. Benz, Aequationes Math. 47 (1994), 79–88.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    R. Narasimhan, Complex Analysis in One Variable, Birkhäuser, Boston, 1985.MATHCrossRefGoogle Scholar
  8. 8.
    A.H. Zemanian, Generalized Integral Transformations, Dover, New York, 1968.MATHGoogle Scholar

Copyright information

© Birkh/:auser Verlag, Basel 1997

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada

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