ArticleOriginal scientific text

Title

The product of a function and a Boehmian

Authors 1

Affiliations

  1. Department of Mathematics, California State University, Stanislaus Turlock, California 95382 U.S.A.

Abstract

Let A be the class of all real-analytic functions and β the class of all Boehmians. We show that there is no continuous operation on β which is ordinary multiplication when restricted to A.

Bibliography

  1. N. K. Bary, A Treatise on Trigonometric Series, Pergamon Press, New York, 1964.
  2. I. M. Gelfand and G. E. Shilov, Generalized Functions, Vol. 2, Academic Press, New York, 1968.
  3. L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, Berlin, 1983.
  4. L. L. Littlejohn and R. P. Kanwal, Distributional solutions of the hypergeometric differential equation, J. Math. Anal. Appl. 122 (1987), 325-345.
  5. J. Mikusiński, Operational Calculus, Pergamon Press, Oxford, 1959.
  6. P. Mikusiński, Convergence of Boehmians, Japan. J. Math. 9 (1983), 159-179.
  7. P. Mikusiński, Boehmians and generalized functions, Acta Math. Hungar. 51 (1988), 271-281.
  8. P. Mikusiński, On harmonic Boehmians, Proc. Amer. Math. Soc. 106 (1989), 447-449.
  9. D. Nemzer, Periodic Boehmians II, Bull. Austral. Math. Soc. 44 (1991), 271-278.
  10. D. Nemzer, The Laplace transform on a class of Boehmians, ibid. 46 (1992), 347-352.
  11. L. Schwartz, Théorie des distributions, Hermann, Paris, 1966.
  12. S. M. Shah and J. Wiener, Distributional and entire solutions of ordinary differential and functional differential equations, Internat. J. Math. and Math. Sci. 6 (1983), 243-270.
  13. J. Wiener, Generalized-function solutions of differential and functional differential equations, J. Math. Anal. Appl. 88 (1982), 170-182.
Pages:
49-55
Main language of publication
English
Received
1992-09-04
Accepted
1993-01-29
Published
1993
Exact and natural sciences