Abstract and Applied Analysis (Jan 2011)

On the Inversion of Bessel Ultrahyperbolic Kernel of Marcel Riesz

  • Darunee Maneetus,
  • Kamsing Nonlaopon

DOI
https://doi.org/10.1155/2011/419157
Journal volume & issue
Vol. 2011

Abstract

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We define the Bessel ultrahyperbolic Marcel Riesz operator on the function f by Uαf=RαB*f, where RαB is Bessel ultrahyperbolic kernel of Marcel Riesz, α…C, the symbol * designates as the convolution, and f∈S, S is the Schwartz space of functions. Our purpose in this paper is to obtain the operator Eα=Uα-1 such that, if Uαf=φ, then Eαφ=f.