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On a testing-function space for distributions associated with the Kontorovich-Lebedev transform.

Semyon B. Yakubovich (2006)

Collectanea Mathematica

We construct a testing function space, which is equipped with the topology that is generated by Lν,p - multinorm of the differential operatorAx = x2 - x d/dx [x d/dx],and its k-th iterates Akx, where k = 0, 1, ... , and A0xφ = φ. Comparing with other testing-function spaces, we introduce in its dual the Kontorovich-Lebedev transformation for distributions with respect to a complex index. The existence, uniqueness, imbedding and inversion properties are investigated. As an application we find a solution...

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

M. Belhadj, Jorge J. Betancor (2004)

Czechoslovak Mathematical Journal

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 ) ' .

On tempered convolution operators

Saleh Abdullah (1994)

Commentationes Mathematicae Universitatis Carolinae

In this paper we show that if S is a convolution operator in S ' , and S * S ' = S ' , then the zeros of the Fourier transform of S are of bounded order. Then we discuss relations between the topologies of the space O c ' of convolution operators on S ' . Finally, we give sufficient conditions for convergence in the space of convolution operators in S ' and in its dual.

On the Fourier transform, Boehmians, and distributions

Dragu Atanasiu, Piotr Mikusiński (2007)

Colloquium Mathematicae

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.

On the Mellin Transforms of Dirac’S Delta Function, The Hausdorff Dimension Function, and The Theorem by Mellin

Südland, Norbert, Baumann, Gerd (2004)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 44A05, 46F12, 28A78We prove that Dirac’s (symmetrical) delta function and the Hausdorff dimension function build up a pair of reciprocal functions. Our reasoning is based on the theorem by Mellin. Applications of the reciprocity relation demonstrate the merit of this approach.

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