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A Kratzel's integral transformation of distributions.

J. A. Barrios, J. J. Betancor (1991)

Collectanea Mathematica

In this paper we study an integral transformation introduced by E. Kratzel in spaces of distributions. This transformation is a generalization of the Laplace transform. We employ the usually called kernel method. Analyticity, boundedness, and inversion theoremes are established for the generalized transformation.

A multidimensional distribution sampling theorem

Francisco Javier González Vieli (2011)

Commentationes Mathematicae Universitatis Carolinae

Using Bochner-Riesz means we get a multidimensional sampling theorem for band-limited functions with polynomial growth, that is, for functions which are the Fourier transform of compactly supported distributions.

A Parseval equation and a generalized finite Hankel transformation

Jorge J. Betancor, Manuel T. Flores (1991)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we study the finite Hankel transformation on spaces of generalized functions by developing a new procedure. We consider two Hankel type integral transformations h μ and h μ * connected by the Parseval equation n = 0 ( h μ f ) ( n ) ( h μ * ϕ ) ( n ) = 0 1 f ( x ) ϕ ( x ) d x . A space S μ of functions and a space L μ of complex sequences are introduced. h μ * is an isomorphism from S μ onto L μ when μ - 1 2 . We propose to define the generalized finite Hankel transform h μ ' f of f S μ ' by ( h μ ' f ) , ( ( h μ * ϕ ) ( n ) ) n = 0 = f , ϕ , for ϕ S μ .

A Phragmén-Lindelöf type quasi-analyticity principle

Grzegorz Łysik (1997)

Studia Mathematica

Quasi-analyticity theorems of Phragmén-Lindelöf type for holomorphic functions of exponential type on a half plane are stated and proved. Spaces of Laplace distributions (ultradistributions) on ℝ are studied and their boundary value representation is given. A generalization of the Painlevé theorem is proved.

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