Displaying similar documents to “A generalized Hankel transformation”

On Hankel transform and Hankel convolution of Beurling type distributions having upper bounded support

M. Belhadj, Jorge J. Betancor (2004)

Czechoslovak Mathematical Journal

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In this paper we study Beurling type distributions in the Hankel setting. We consider the space ℰ ( w ) ' of Beurling type distributions on ( 0 , ∞ ) having upper bounded support. The Hankel transform and the Hankel convolution are studied on the space ℰ ( w ) ' . We also establish Paley Wiener type theorems for Hankel transformations of distributions in ℰ ( w ) ' .

A Parseval equation and a generalized finite Hankel transformation

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

Commentationes Mathematicae Universitatis Carolinae

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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 .