WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 1Citation - Scopus: 1On the Non-Commutative Neutrix Product of the Distributions X<sup>-r</Sup>+ Ln<sup>p</Sup> X+ and X<sup>μ</Sup>+ln<sup>q< X+(Taylor & Francis Ltd, 2006) Tas, Kenan; Fisher, BrianLet f and g be distributions and g(n) = (g*delta(n))(x), where delta(n)(x ) is a certain sequence converging to the Dirac delta-function. The non-commutative neutrix product f o g of f and g is defined to be the neutrix limit of the sequence {fg(n) }, provided its limit h exists in the sense that [GRAPHICS] for all functions phi in D. It is proved that (x(+)(-r) ln(p) x(+)) o (x(+)(mu) ln(q) x(+)) = x(+)(-r+mu) ln(p+q) x(+) (x(-)(-r) ln(p) (x)-) o (x(-)(mu) ln(q) x(-)) = x(-)(-r+mu) ln(p+q) x(-) for mu < r - 1;mu not equal 0, +/- 1, +/- 2,..., r = 1,2,..., and p, q = 0, 1, 2,....Article Citation - WoS: 3Citation - Scopus: 1On the Non-Commutative Neutrix Product of the Distributions X<sup>r</Sup> Ln<sup>p</Sup> | X | and X<sup>-s</Sup>(Taylor & Francis Ltd, 2005) Tas, K; Fisher, BThe 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,....Article Citation - WoS: 5Citation - Scopus: 5On the Composition of the Distributions X<sup>-1</Sup> Ln|x| and X+<sup>r</Sup>(Taylor & Francis Ltd, 2005) Fisher, B; Tas, KLet 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.....Article Citation - WoS: 1Citation - Scopus: 2Some Results on the Non-Commutative Neutrix Product of Distributions(Taylor & Francis Ltd, 2009) Tas, Kenan; Fisher, BrianIt is proved that the non-commutative neutrix product of the distributions x-r and xslnq|x| exists and [image omitted] for r, q=1, 2, , s=0,1,2, and r-s1.Article Commutative Convolution of Functions and Distributions(Taylor & Francis Ltd, 2007) Tas, Kenan; Fisher, BrianThe commutative convolution f * g of two distributions f and g in D' is defined as the limit of the sequence {(f tau(n)) * (g tau(n))}, provided the limit exists, where {tau(n)} is a certain sequence of functions tn in D converging to 1. It is proved that |x|(lambda) * (sgn x|x|(-lambda-1)) = pi[cot (pi lambda) - cosec(pi lambda)] sgn x|x|(0), for lambda not equal 0, +/- 1, +/- 2, ... , where B denotes the Beta function.