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Transforms of Boehmians

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Abstrakty
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 Abstract: Boehmians are defined by an algebraic construction which is similar to the construction of a field of quotients. If the construction is applied to a function space and the multiplication is interpreted as convolution, the construction yields a space of generalized functions. Those spaces provide a natural setting for extensions of transforms like the Fourier, Laplace, Radon, or Zak transforms. Since the abstract algebraic definition of Boehmians allows different interpretations, not necessarily based on the convolution product, those transforms are actually isomorphisms between spaces of Boehmians.
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Twórcy
  • Department of Mathematics, University of Central Florida, Orlando, Florida 32816-1364, U.S.A.
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Bibliografia
[1] T. K. Boehme, The support of Mikusiński operators, Trans. Amer. Math. Soc. 176 (1973), 319-334.
[2] J. Mikusiński, Operational Calculus, Pergamon Press, New York, 1959.
[3] J. Mikusiński et P. Mikusiński, Quotients de suites et leurs applications dans l'analyse fonctionnelle, C. R. Acad. Sci. Paris Sér. I 293 (1981), 463-464.
[4] P. Mikusiński, Convergence of Boehmians, Japan. J. Math. 9 (1983), 159-179.
[5] P. Mikusiński, Fourier transform for integrable Boehmians, Rocky Mountain J. Math. 17 (1987), 577-582.
[6] P. Mikusiński, Boehmians and generalized functions, Acta Math. Hungar. 51 (1988), 271-281.
[7] P. Mikusiński, Boehmians on open sets, ibid. 55 (1990), 63-73.
[8] P. Mikusiński, The Fourier transform of tempered Boehmians, in: Fourier Analysis: Analytic and Geometric Aspects, Lecture Notes in Pure and Appl. Math., Marcel Dekker, New York, 1994, 303-309.
[9] P. Mikusiński, Tempered Boehmians and ultradistributions, Proc. Amer. Math. Soc., to appear.
[10] P. Mikusiński, A. Morse, and D. Nemzer, The two-sided Laplace transform for Boehmians, Integral Transforms and Special Functions 2 (1994), 219-230.
[11] P. Mikusiński and A. Zayed, The Radon transform of Boehmians, Proc. Amer. Math. Soc. 118 (1993), 561-570.
[12] P. Mikusiński and A. Zayed, An extension of the Radon transform, in: Proc. of International Symposium on Generalized Functions, Banaras Hindu University, India 1991, Plenum Press, New York, 1993, 141-147.
[13] M. Morimoto and P. Mikusiński, Boehmians on the sphere, preprint.
[14] A. Zayed and P. Mikusiński, On the extension of the Zak transform, Methods Appl. Anal., to appear.
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DML-PL
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