In this paper we apply a method of spectral theory of linear operators [10] to establish relations between the support of a function f on R with properties of its image Tf under a linear operator T : R → R. The classical approach uses analytic continuation of the image Tf into some complex domain (theorems of Paley-Wiener type [4, 5, 6, 7]), and therefore, could not apply to functions whose ima...

A class ξ of algebras of symmetric n × n matrices, related to Toeplitz-plus-Hankel structures and including the well-known algebra H diagonalized by the Hartley transform, is investigated. The algebras of ξ are then exploited in a general displacement decomposition of an arbitrary n× n matrix A. Any algebra of ξ is a 1-space, i.e., it is spanned by n matrices having as first rows the vectors of...

Connections between Hankel transforms of different order for L-functions are examined. Well known are the results of Guy [Guy] and Schindler [Sch]. Further relations result from projection formulae for Bessel functions of different order. Consequences for Hankel multipliers are exhibited and implications for radial Fourier multipliers on Euclidean spaces of different dimensions indicated.

The mode-matching applications to scattering from circular and annular apertures in a thick perfectly conducting plane are reviewed. The Hankel and Weber transforms are utilized to solve the boundary-value problems of circular and annular apertures. Simple electrostatic problems are presented to illustrate the mode-matching method in terms of the Hankel and Weber transforms. Various types of We...

In this presentation we establish new bounds on functions, which have their n-th order Hankel Transform bandlimited. This class of functions is proved to be also Fourier Transform bandlimited. N-th order Hankel Transforms and the consequent bounds are important for the reconstruction in CAT, MRI (Magnetic Resonance Imaging) etc. Indeed many algorithms of modern tomography use the appropriate fo...

It is well known that the Hankel transform possesses neither a shift-modulation nor a convolution-multiplication rule, both of which have found many uses when used with other integral transforms. In this paper, the generalized shift operator, as defined by Levitan, is applied to the Hankel transform. It is shown that under this generalized definition of shift, both convolution and shift theorem...