Browsing by Author "Fisher, B"

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On the composition of the distributions x(+)(lambda) and x(+)(mu)
(Academic Press inc Elsevier Science, 2006) Fisher, B; Taş, Kenan; 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 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.
On the composition of the distributions x(-1) ln vertical bar x vertical bar 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.....
On the non-commutative neutrix product of the distributions x(r) ln(P) vertical bar x vertical bar and x(-s)
(Taylor & Francis Ltd, 2005) Fisher, B; Taş, Kenan; Tas, K; 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,....
The convolution of functions and distributions
(Academic Press inc Elsevier Science, 2005) Fisher, B; Taş, Kenan; Tas, K; 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.