Browsing by Author "Fisher, B"

Now showing 1 - 5 of 5

Citation - WoS: 9
Citation - Scopus: 13
The Convolution of Functions and Distributions
(Academic Press inc Elsevier Science, 2005) Tas, K; Fisher, B; 4971
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.
Citation - WoS: 2
Citation - Scopus: 2
On the Commutative Product of Distributions
(Korean Mathematical Soc, 2006) Tas, K; Fisher, B; 4971
The commutative products of the distributions x(r) ln(p) vertical bar x vertical bar and x(-r-1) ln(q) vertical bar x vertical bar and of sgn x x(r) ln(P) vertical bar x vertical bar and sgn x x(-r-1) ln(q) vertical bar x vertical bar are evaluated for r = 0, +/- 1, +/- 2,... and p, q = 0, 1, 2,....
Citation - WoS: 5
Citation - Scopus: 5
On the Composition of the Distributions X^-1 Ln|x| and X+^r
(Taylor & Francis Ltd, 2005) Fisher, B; Tas, K; 4971
Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {F-n(f)}, where 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 (x). The distribution (x(+)(r))(-1) ln \x(+)(r)\ is evaluated for r = 1, 2.....
Citation - WoS: 3
Citation - Scopus: 1
On the Non-Commutative Neutrix Product of the Distributions X^r Ln^p | X | and X^-s
(Taylor & Francis Ltd, 2005) Tas, K; Fisher, B; 4971
The non-commutative neutrix product of the distributions x(r) ln(P) \x\ and x(-s) is evaluated for r - s -2. -3,..../ p = 1, 2,....
Citation - WoS: 5
Retracted: on the Composition of the Distributions X+^λ and X+^μ (Retracted Article. See Vol. 330, Pg. 1494 2007)
(Academic Press inc Elsevier Science, 2006) Tas, K; Fisher, B; 4971
Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {F-n(f)}, where 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 distributions (x(+)(mu) )(+)(lambda) are evaluated for lambda < 0, mu > 0 and lambda, lambda mu not equal -1, -2.... (c) 2005 Elsevier Inc. All rights reserved.