WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 5Citation - Scopus: 5On the Composition of the Distributions X+-R and X+μ(indian Nat Sci Acad, 2005) Fisher, B.; Tas, K.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 Fn (x) = F (x) * δn (x) and {δn (x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta function δ (x). The distribution (x+μ)+-r and ( l x lμ)+-r are evaluated for μ > 0, r = 1, 2, ..., and kμ ≠ 1, 2,... © Printed in India.Article Citation - WoS: 3Citation - Scopus: 2On the Non-Commutative Neutrix Product of the Distributions X<sup>λ</Sup>+ and X<sup>μ</Sup>+(Springer Heidelberg, 2006) Tas, K.; Fisher, B.Let f and g be distributions and let 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 circle g of f and g is defined to be the limit of the sequence {fg(n)}, provided its limit h exists in the sense that [GRAPHICS] for all functions p in D. It is proved that (x(+)(lambda)ln(p)x(+)) circle (x(+)(mu)ln(q)x(+)) = x(+)(lambda+mu)ln(p+q)x(+), (x(-)(lambda)ln(p)x(-)) circle (x(-)mu ln(q)x(-)) = x(-)(lambda+mu)ln(p+q)x(-), for lambda + mu < -1; lambda,mu,lambda+mu not equal -1,-2,... and p,q = 0,1,2.....Article On the non-commutative neutrix product of the distributions x(+)(lambda) and x(+)(mu)(Springer Heidelberg, 2006) Fisher, Brian; Taş, KenanLet f and g be distributions and let 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 circle g of f and g is defined to be the limit of the sequence {fg(n)}, provided its limit h exists in the sense that [GRAPHICS] for all functions p in D. It is proved that (x(+)(lambda)ln(p)x(+)) circle (x(+)(mu)ln(q)x(+)) = x(+)(lambda+mu)ln(p+q)x(+), (x(-)(lambda)ln(p)x(-)) circle (x(-)mu ln(q)x(-)) = x(-)(lambda+mu)ln(p+q)x(-), for lambda + mu < -1; lambda,mu,lambda+mu not equal -1,-2,... and p,q = 0,1,2.....Article Citation - WoS: 2Citation - Scopus: 2On the Commutative Product of Distributions(Korean Mathematical Soc, 2006) Tas, K; Fisher, BThe 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,....