Fourier analysis on locally convex spaces of distributions, II

• Autorzy: Sinha R. P. , Mohammed A. N.
• Języki publikacji: EN

Abstrakty

EN

This is the second in a series of papers, extending the theory of Fourier analysis to locally convex spaces of distributions (LCD-spaces). In this paper, LCD-spaces admitting conjugation and multiplier operators on LCD-spaces are discussed. It is also shown that if E is an LCD-space having C∞ as a dense subset, then E*, endowed with the topology of precompact convergence, is an LCD-space having C∞ as a dense subset.

Słowa kluczowe

EN

Fourier analysis; convex spaces; topological vector spaces

PL

analiza Fouriera; przestrzeń wypukła

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 4
• Strony: 899--913
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Sinha R. P.

• Department of Mathematics, I. I. T. Roorkee, Roorkee, India - 247667

autor

Mohammed A. N.

• Dubai University College, General Education Department, P.O. Box 14143, Dubai, United Arab Emirates UAE

Bibliografia

• [1] R. E. Edwards, Fourier Series, Vols. I, II, Springer-Verlag, New York, 1979, 1982.
• [2] L. Narici and E. Beckenstein, Topological Vector Spaces, Marcel Dekker, Inc. New York, 1985.
• [3] M. P. Singh, On Frechet Spaces of Distributions and Multiplier Operators, Ph.D. Thesis, University of Roorkee, Roorkee, 1991.
• [4] R. P. Sinha, Reflexive locally convex spaces of distributions are homogeneous, Bull. Soc. Math. Belg., Ser. B, 44 (1992), No. 1, 83-87.
• [5] R. P. Sinha, Vishnu Kant, On the Banach space of distributions, Bull. Soc. Math. Belg., Ser. B, 41 (1989), No. 3, 295-305.
• [6] R. P. Sinha, A. N. Mohammed, Fourier analysis on locally convex spaces of distributions I, Demonstratio Math. 36 (2003), No 3, 697-709.
• [7] A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, Inc., New York, 1978.
• [8] M. Zamansky, Sur l¹ approximation fonctiones continues periodiques, C.R. Acad. Sci., Paris, 228 (1949), MR10, 449; 460-461.
• [9] A. Zygmund, Trigonometric Series, Vols. I and II, Cambridge University Press, New York, 1968.