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Mapping Properties and Composition Structure of Multidimensional Integral Transforms
Author(s) -
Glaeske HansJürgen,
Tuan Vu Kim
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.19911520116
Subject(s) - mathematics , composition (language) , pure mathematics , fourier transform , constant (computer programming) , type (biology) , mathematical analysis , function (biology) , value (mathematics) , statistics , ecology , philosophy , linguistics , evolutionary biology , computer science , biology , programming language
In this paper mapping properties of multidimensional integral transforms ℑ are considered, which have a composition of the type ℑ f = C ℑ a ℑ f , where C is a constant, ℑ the Fourier transform and a denotes a function of absolute value one. Mapping properties are investigated in the spaces L 2 (R n ) and in Lizorkin spaces of test and generalized functions as well as in Gelfand‐Shilov spaces of test and generalized functions. Two‐ and three‐dimensional examples are discussed.