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Displaying similar documents to “Inversion integrals for the integral transforms involving the Meijer’s G -function as kernel”

On integral transforms.

Gupta, K.C. (1982)

International Journal of Mathematics and Mathematical Sciences

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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 .