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The KRÄTZEL Integral Transformation of Distributions
Author(s) -
Barrios Javier A.,
Betancor Jorge J.
Publication year - 1991
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19911540103
Subject(s) - mathematics , transformation (genetics) , laplace transform , extension (predicate logic) , isomorphism (crystallography) , mellin transform , pure mathematics , integral transform , riesz transform , algebra over a field , mathematical analysis , biochemistry , chemistry , computer science , crystal structure , crystallography , gene , programming language
In this paper we define an integral transformation, introduced by E. KRÄTZEL and denoted by Σ v ( n )that is an extension of the LAPLACE transformation in certain spaces of generalized functions. We employ a procedure based on adjoint operators. We first show that the classical integral transformation is an isomorphism between two new FRÉCHET function spaces. Later the generalized Σ v ( n )transformation is defined over the corresponding dual spaces as the adjoint of the classical transform. The MELLIN integral transformation is a very useful tool in our study.