Titlebook: Generalized Functions and Their Applications; R. S. Pathak Book 1993 Springer Science+Business Media New York 1993 Manifold.Standard.diffe

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Andrew Junor,Damian Gleeson,Susan MaysonSince the publication of Schwartz’s work on the theory of distributions (Schwartz, 1950–1951), in particular his work on the Fourier transform of distributions, there has been a tremendous influx of research papers on integral transforms of generalized functions. One of the main sources on this topic is the book by Zemanian (1968).

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Cauchy Representation of Distributions and Applications to Probability II,The Cauchy representation of distributions in the space (..(..))’ is proved. It is shown that every probability density defines a generalized function on the space ..(..) (1 < p < ∞) of test functions. Application of these results in probability theory are discussed.

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An Extension of the Radon Transform,Since the publication of Schwartz’s work on the theory of distributions (Schwartz, 1950–1951), in particular his work on the Fourier transform of distributions, there has been a tremendous influx of research papers on integral transforms of generalized functions. One of the main sources on this topic is the book by Zemanian (1968).

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Svetlana Yarosh,Gregory D. Abowdhe standard Bergman class ..(.), consisting of functions analytic on the open unit disk . and square-summable with respect to the area measure. As the functions in .. (.) usually have boundary values only in the sense of Schwartz distributions, so we are led to the notion of Toeplitz operators acting on distributions.