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J. Korean Math. Soc. 2000; 37(3): 371-389
Printed May 1, 2000
Copyright © The Korean Mathematical Society.
Localization and multiplication of distributions
Ian Richards and Heekyung K. Youn
University of St. Thomas and University of Minnesota
Working within classical distribution theory, we develop notions of multiplication and convolution for tempered distributions which are general enough to encompass the classical cases -- such as pointwise multiplication of continuous functions or the convolution of $L^1$ functions -- which most textbook treatments of distribution theory leave out. Pains are taken to develop a theory which satisfies the commutative and associative laws.
Keywords: tempered distributions, localization, multiplication, Fourier transform, partial integration, convolution
MSC numbers: 46F30
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