On the non-commutative neutrix product of the distributions χ+γ and χ+μ

Fisher B., TAŞ K.

Acta Mathematica Sinica, English Series, vol.22, no.6, pp.1639-1644, 2006 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 6
  • Publication Date: 2006
  • Doi Number: 10.1007/s10114-005-0762-7
  • Journal Name: Acta Mathematica Sinica, English Series
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1639-1644
  • Keywords: Delta function, Distribution, Product of distributions
  • Uşak University Affiliated: No

Abstract

Let f and g be distributions and let gn = (g * δn)(x), where δn(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 limit of the sequence {fg n}, provided its limit h exists in the sense that N-lim = , n → ∞ for all functions ≁ in script D. It is proved that (x+λln px+) o (x+μlnpx + = x+λ+μlnp+qx +, (x-λlnpx- o (x-μlnqx- = (x- λ+μlnp+qx-, for λ + μ < - 1; λ, μ, λ + μ ≠ -1, -2, ... and p, q = 0, 1, 2..... © 2006 Springer-Verlag.