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Mean-periodic functions

Author

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  • Carlos A. Berenstein
  • B. A. Taylor

Abstract

We show that any mean-periodic function f can be represented in terms of exponential-polynomial solutions of the same convolution equation f satisfies, i.e., u ∗ f = 0 ( μ ∈ E ′ ( ℠n ) ) . This extends to n -variables the work of L . Schwartz on mean-periodicity and also extends L . Ehrenpreis' work on partial differential equations with constant coefficients to arbitrary convolutors. We also answer a number of open questions about mean-periodic functions of one variable. The basic ingredient is our work on interpolation by entire functions in one and several complex variables.

Suggested Citation

  • Carlos A. Berenstein & B. A. Taylor, 1980. "Mean-periodic functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 3, pages 1-37, January.
    • Handle: RePEc:hin:jijmms:574732
    DOI: 10.1155/S0161171280000154
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