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

Fisher B., TAŞ K.

Acta Mathematica Sinica, English Series, cilt.22, sa.6, ss.1639-1644, 2006 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 6
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1007/s10114-005-0762-7
  • Dergi Adı: Acta Mathematica Sinica, English Series
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1639-1644
  • Anahtar Kelimeler: Delta function, Distribution, Product of distributions
  • Uşak Üniversitesi Adresli: Hayır

Özet

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.