Structure theorems for associated homogeneous distributions based on the line
Associated homogeneous distribution
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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.
CitationFranssens, G.R. (2009). Structure theorems for associated homogeneous distributions based on the line. , Mathematical Methods in the Applied Sciences, Vol. 32, Issue 8, 986-1010, DOI: 10.1002/mma.1078.