Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9503189 | Journal of Mathematical Analysis and Applications | 2005 | 11 Pages |
Abstract
The non-commutative convolution fâg of two distributions f and g in Dâ² is defined to be the limit of the sequence {(fÏn)âg}, provided the limit exists, where {Ïn} is a certain sequence of functions in D converging to 1. It is proved that |x|λâ(sgnx|x|μ)=2sin(λÏ/2)cos(μÏ/2)sin[(λ+μ)Ï/2]B(λ+1,μ+1)sgnx|x|λ+μ+1, for â1<λ+μ<0 and λ,μâ â1,â2,â¦, where B denotes the Beta function.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Brian Fisher, Kenan TaÅ,