Kyungpook Mathematical Journal

  • 제47권4호
  • /
  • Pages.481-493
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  • 2007
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지

The Cauchy Representation of Integrable and Tempered Boehmians

  • 투고 : 2005.10.05
  • 발행 : 2007.12.23
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초록

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.

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참고문헌

  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.