Accession Number : AD0623124

Title :   THE DISTRIBUTIONAL HANKEL TRANSFORMATION.

Descriptive Note : Scientific rept.,

Corporate Author : STATE UNIV OF NEW YORK STONY BROOK COLL OF ENGINEERING

Personal Author(s) : Zemanian,A. H.

Report Date : 09 AUG 1965

Pagination or Media Count : 61

Abstract : The Hankel transformation is generalized in a distributional way, something that apparently has not been done before. Two different procedures are used to accomplish this. In the first procedure a topological linear space of testing functions is constructed for which the mu-th order Hankel transformation is a topological automorphism. The dual space consists of the mu-th order Hankel-transformable distributions. The distributional Hankel transformation is then defined by generalizing a variation of Parseval's formula. It turns out that the distributions to which this transformation may be applied must be of slow growth. The second procedure yields a more general result in that there is no restriction on the rate of growth of the distributions that are to be transformed. Here again, Parseval's formula is used to define the generalized Hankel transformation, but in contrast to the previous case the testing functions for the distributions under consideration are required to have bounded supports. The Hankel transforms then turn out to be continuous linear functionals on certain classes of analytic functions. Several applications to differential equations containing Bessel-type differential operators are also given. (Author)

Descriptors :   (*INTEGRAL TRANSFORMS, DISTRIBUTION THEORY), (*DISTRIBUTION THEORY, INTEGRAL TRANSFORMS), TOPOLOGY, FUNCTIONAL ANALYSIS, OPERATORS(MATHEMATICS)

Distribution Statement : APPROVED FOR PUBLIC RELEASE