Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T16:12:51.224Z Has data issue: false hasContentIssue false
  • English
  • Français

Periodic Boehmians II

Published online by Cambridge University Press:  17 April 2009

Dennis Nemzer
Dennis Nemzer
Affiliation:
Department of Mathematics, California State University, Stanislaus, Turlock California 95380, United States of America
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A space of periodic generalised functions, called boehmians, is investigated. The space of boehmians contains all periodic distributions. It is known that not every hyperfunction is a boehmian. We show that the converse is also true. We present some theorems which give sufficient conditions for a sequence of complex numbers to be the Fourier coefficients of a boehmian. Sufficient conditions (in terms of the Fourier coefficients) are obtained for a sequence of boehmians to converge. As an application, a Dirichlet problem is discussed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 2 , October 1991 , pp. 271 - 278
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Boehme, T.K. and Wygant, G., ‘Generalized functions on the unit circle’, Amer. Math. Monthly 82 (1975), 256–261.Google Scholar
[2]Collier, M.G. and Kelingos, J.A., ‘Periodic Beurling distributions’, Acta. Math. Hungar. 42 (1983), 261–278.Google Scholar
[3]Gorbacuk, V.I. and Gorbacuk, M.L., ‘Trigonometric series and generalized periodic functions’, Soviet Math. Dokl. 23 (1981), 342–346.Google Scholar
[4]Johnson, G., ‘Harmonic functions on the unit disk’, Illinois J. Math. 12 (1968), 366–385.Google Scholar
[5]Mikusinski, P., ‘Convergence of Boehmians’, Japan J. Math. 9 (1983), 159–179.Google Scholar
[6]Nemzer, D., ‘Periodic Boehmians’, Internat. J. Math. Math. Sci. 12 (1989), 685–692.Google Scholar
[7]Nemzer, D., ‘Periodic generalized functions’, Rocky Mountain J. Math. 20 (1990).Google Scholar
[8]Schwartz, L., Theorie des distributions (Herman, Paris, 1966).Google Scholar