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Structure theorems for associated homogeneous distributions based on the line

✍ Scribed by Ghislain R. Franssens

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 211 KB
Volume: 32
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1078

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✦ Synopsis

Abstract

Associated homogeneous distributions (AHDs) with support in the line R are the distributional generalizations of one‐dimensional power‐log functions. In this paper, we derive a number of practical structure theorems for AHDs based on R and being complex analytic with respect to their degree of homogeneity in some region of the complex plane. Each theorem gives a representation that is designed to have a distinct advantage for calculating either convolution products, multiplication products, generalized derivatives and primitives, Fourier transforms or Hilbert transforms of AHDs. Copyright © 2008 John Wiley & Sons, Ltd.

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