Fourier analysis on Colombeau's algebra of generalized functions

Journal d'Analyse Mathematique

Volumn 69, Issue , 1996, Pages 201-227

  Soraggi, Roberto Luiz ^a  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040656024     PISSN: 00217670     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02787107     Document Type: Article

References (12)

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2. H. A. Biagioni, A non-linear theory of generalized functions, Lecture Notes in Mathematics 1421, Springer-Verlag, Berlin, 1990.
3. J. F. Colombeau, New Generalized Functions and Multiplication of Distributions, North-Holland Math. Studies 84, 1984.
4. J. F. Colombeau, Elementary Introduction to New Generalized Functions, North-Holland Math. Studies 113, 1985.
5. J. Horváth, Topological Vectors Spaces and Distributions, Volume I, Addison-Wesley Series in Math., 1966.
6. V. Karunakaran and A. Vijayan, Laplace transforms of generalized functions, Houston J. Math. 19 (1993), 75-88.
7. R. E. A. C. Paley and N. Wiener, Fourier transforms in the complex domain, Amer. Math. Soc. Colloquium, Publ. XIX, New York, 1934.
8. L. Nachbin, Lecture on the theory of distributions, Textos de Matemática, Instituto de Física e Matemática, Universidade do Recife, 1964. (Reprinted by University Microfilms International (USA) 1980.)
9. M. Nedeljkov and S. Pilipović, Paley-Wiener type theorems for Colombeau's generalized functions, J. Math. Anal. Appl. 195 (1995), 108-122.
10. Ya. V. Radyno, Ngo Fu Tkhan and Sabra Ramadan, The Fourier transform in an algebra of new generalized functions, Russian Acad. Sci. Dokl. Math. 46, No. 3 (1993), 414-417.
11. W. Rudin, Functional Analysis, McGraw Hill, New York, 1973.
12. L. Schwartz, Théorie des distributions, Vol. II, Hermann, Paris, 1951.