Acta Applicandae Mathematicae

, Volume 98, Issue 2, pp 135–152 | Cite as

On a Certain Class of Integral Equations Associated with Hankel Transforms

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Abstract

This paper deals with a new class of Fredholm integral equations of the first kind associated with Hankel transforms of integer order. Analysis of the equations is based on operators transforming Bessel functions of the first kind into kernels of Weber–Orr integral transforms. Their inverse operators are established by means of new inversion theorems for the Hankel and Weber–Orr integral transforms of functions belonging to L 1 and L 2. These operators together with the proven Paley–Wiener’s theorem for the Weber–Orr transform enable to regularize the equations and, in special cases, to derive explicit solutions. The integral equations analyzed in this paper can be employed instead of dual integral equations usually treated with the Cooke–Lebedev method. An example manifests that it may be preferable because of the possibility to control norms of operators in the regularized equations.

Keywords

Fredholm integral equation Dual integral equations Hankel transform Weber–Orr transform Paley–Wiener theorem 

Mathematics Subject Classification (2000)

45B05 45F10 44A15 
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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Communication Engineering and Center for Appl. Indust. Mathematics at Department of SciencesHIT-Holon Institute of TechnologyHolonIsrael

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