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Structure theorems for associated homogeneous distributions based on the line
Author(s) -
Franssens Ghislain R.
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1078
Subject(s) - mathematics , homogeneity (statistics) , convolution (computer science) , homogeneous , complex plane , multiplication (music) , fourier transform , pure mathematics , representation (politics) , mathematical analysis , combinatorics , statistics , computer science , machine learning , artificial neural network , politics , political science , law
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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