The product of a function and a Boehmian

• Autorzy: Dennis Nemzer
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1993
• Tom: 66
• Numer: 1
• Strony: 49-55

Daty

wydano

1993

otrzymano

1992-09-04

poprawiono

1993-01-29

Twórcy

autor

Dennis Nemzer

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

Bibliografia

• [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.