The Fourier transform of distributions and the exchange formula
B. Fisher, Li Chen Kuan, A. Takači (1988)
Matematički Vesnik
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Displaying similar documents to “On some classes of infinitely decomposable Sobolev-Schwartz test functions”
The Fourier transform of distributions and the exchange formula
A characterization of Fourier transforms
Philippe Jaming (2010)
Colloquium Mathematicae
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The aim of this paper is to show that, in various situations, the only continuous linear (or not) map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups ℤ/nℤ, the integers ℤ, the torus 𝕋 and the real line. We also ask a related question for the twisted convolution.
Convolution in Colombeau's Spaces of Generalized Functions; Part I: the Space Ga and the A-integral
Marko Nedeljkov, Stevan Pilipović (1992)
Publications de l'Institut Mathématique
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Convolution in Colombeau's spaces of generalized functions. II: The convolution in .
Nedeljkov, M., Pilipović, S. (1992)
Publications de l'Institut Mathématique. Nouvelle Série
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On the polyconvolution with the weight function for the Fourier cosine, Fourier sine, and the Kontorovich-Lebedev integral transforms.
Nguyen Xuan Thao (2010)
Mathematical Problems in Engineering
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On the Fourier transform, Boehmians, and distributions
Dragu Atanasiu, Piotr Mikusiński (2007)
Colloquium Mathematicae
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We introduce some spaces of generalized functions that are defined as generalized quotients and Boehmians. The spaces provide simple and natural frameworks for extensions of the Fourier transform.
A note on the convolution in the Mellin sense with generalized functions.
Kilicman, Adem, Kamel Ariffin, Muhammad Rezal (2002)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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The Fourier transofrm technique for convolution equations in infinite dimensional lq-spaces.
Alexander L. Koldobskii (1991)
Mathematische Annalen
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Bernoulli convolutions-an application of set theory in analysis
Robert Kaufman (1990)
Colloquium Mathematicae
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On a generalization of the convolution
E. Gesztelyi (1970)
Annales Polonici Mathematici
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Fourier transforms of convolution operators
Charles Swartz (1973)
Studia Mathematica
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On Fourier coefficients and factorable operators.
Faragallah, M., Elshobaky, E. (2002)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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On the support of Fourier transform of weighted distributions
Martha Guzmán-Partida (2010)
Commentationes Mathematicae Universitatis Carolinae
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We give sufficient conditions for the support of the Fourier transform of a certain class of weighted integrable distributions to lie in the region and .