The convolution of functions and distributions

被引：9

作者：

Fisher, B ^{[1
]}

Tas, K

机构：

[1] Univ Leicester, Dept Math, Leicester LE1 7RH, Leics, England

[2] Cankaya Univ, Dept Math, Ankara, Turkey

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2005年 / 306卷 / 01期

关键词：

distribution; dirac delta function; convolution;

D O I：

10.1016/j.jmaa.2005.01.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The non-commutative convolution f * g of two distributions f and g in V is defined to be the limit of the sequence {(f tau(n)) * g}, provided the limit exists, where {tau(n)} is a certain sequence of functions in D converging to 1. It is proved that vertical bar x vertical bar(lambda) * (sgnx vertical bar x vertical bar(mu)) = 2 sin(lambda pi/2)cos(mu pi/2)/sin[(lambda+mu)pi/2] B(lambda+1, mu+1) sgn x vertical bar x vertical bar(lambda+mu+1), for -1 < lambda + mu < 0 and lambda, mu not equal -1, -2,..., where B denotes the Beta function. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：364 / 374

页数：11