The distribution composition (x(+)(r))(-s)

Authors
Nicholas, JD Fisher, B
Citation
Jd. Nicholas et B. Fisher, The distribution composition (x(+)(r))(-s), J MATH ANAL, 258(1), 2001, pp. 131-145
Citations number
6
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN journal
0022247X → ACNP
Volume
258
Issue
1
Year of publication
2001
Pages
131 - 145
Database
ISI
SICI code
0022-247X(20010601)258:1<131:TDC(>2.0.ZU;2-X
Abstract
Let F be a distribution and let f be a locally summable function. The distr ibution F(f) is defined as the neutrix limit of the sequence {F-n(f)}, wher e F-n(x) = F(x)(*) delta (n)(x) and {delta (n)(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta function delta (x). The distribution (x(+)(r))(-s) is evaluated for r, s = 1, 2,... Further results are deduced. (C) 2001 Academic Press.