Tas, KFisher, B2020-04-162025-09-182020-04-162025-09-182005Fisher, B.; Taş, K., "The convolution of functions and distributions", Journal Of Mathematical Analysis And Applications, Vol.306, No.1, pp.364-374, (2005).0022-247X1096-0813https://doi.org/10.1016/j.jmaa.2005.01.004https://hdl.handle.net/123456789/10464Tas, Kenan/0000-0001-8173-453XThe 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.eninfo:eu-repo/semantics/closedAccessDistributionDirac Delta FunctionConvolutionArticle10.1016/j.jmaa.2005.01.0042-s2.0-16344379404