Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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The Cauchy Representation of Integrable and Tempered Boehmians

  • Received : 2005.10.05
  • Published : 2007.12.23
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Abstract

This paper deals with, by employing the relation between Cauchy representation and the Fourier transform and properties of the former in $L_1$-space, the investigation of the Cauchy representation of integrable Boehmians as a natural extension of tempered distributions, we have investigated Cauchy representation of tempered Boehmians. An inversion formula is also proved.

Keywords

References

  1. H. Bremermann, Distributions, Complex Variables and Fourier transforms, Addison- Wesley Publishing Company, Inc., Reading, Mass, 1965.
  2. J. Mikusinski and P. Mikusinski, Quotients de suites leures applications dans l analyse fonctionelle, Comptes Rendus, 293(I)(1981), 463-464.
  3. P. Mikusinski, Convergence of Boehmians, Japan J. Math., 9(1983), 159-179. https://doi.org/10.4099/math1924.9.159
  4. P. Mikusinski, Fourier transform for integrable Boehmians, Rocky Mountain J. Math., 17(3)(1987), 577-582. https://doi.org/10.1216/RMJ-1987-17-3-577
  5. P. Mikusinski, The Fourier transform of Tempered Boehmians, Fourier Analysis, Lecture Notes in Pure and Appl. Math., Marcel Dekker, New York (1944), 303-309.
  6. D. Nemzer, The Boehmians as an F-Space. Doctoral Thesis, University of California, Santa Barbara, 1984.