On the Inversion of Bessel Ultrahyperbolic Kernel of Marcel Riesz

Darunee Maneetus and Kamsing Nonlaopon

Abstract and Applied Analysis, 2011, vol. 2011, 1-13

Abstract:

We define the Bessel ultrahyperbolic Marcel Riesz operator on the function ð ‘“ by 𠑈 ð ›¼ ( ð ‘“ ) = ð ‘… ð µ ð ›¼ ∗ ð ‘“ , where ð ‘… ð µ ð ›¼ is Bessel ultrahyperbolic kernel of Marcel Riesz, ð ›¼ … â„‚ , the symbol ∗ designates as the convolution, and ð ‘“ ∈ ð ’® , ð ’® is the Schwartz space of functions. Our purpose in this paper is to obtain the operator ð ¸ ð ›¼ = ( 𠑈 ð ›¼ ) − 1 such that, if 𠑈 ð ›¼ ( ð ‘“ ) = 𠜑 , then ð ¸ ð ›¼ 𠜑 = ð ‘“ .

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:419157

DOI: 10.1155/2011/419157

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