The convolution of functions and distributions

Fisher B., TAŞ K.

Journal of Mathematical Analysis and Applications, cilt.306, sa.1, ss.364-374, 2005 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 306 Sayı: 1
  • Basım Tarihi: 2005
  • Doi Numarası: 10.1016/j.jmaa.2005.01.004
  • Dergi Adı: Journal of Mathematical Analysis and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.364-374
  • Anahtar Kelimeler: Convolution, Dirac delta function, Distribution
  • Uşak Üniversitesi Adresli: Hayır

Özet

The non-commutative convolution f * g of two distributions f and g in D′ is defined to be the limit of the sequence {(fτn) * g}, provided the limit exists, where {τn} is a certain sequence of functions in D converging to 1. It is proved that x λ * (sgnx x μ) = 2 sin(λπ/2)cos(μπ/2)/sin[(λ + μ)π/2] B(λ + 1, μ + 1) sgn x x λ+μ+1, for - 1 < λ + μ < 0 and λ, μ≠ - 1, - 2,..., where B denotes the Beta function. © 2005 Elsevier Inc. All rights reserved.