The Journal of the Indian Mathematical Society

The Pseudo-Differential Type Operator and Hankel Type Transformation Associated with Bessel Type Operator


Affiliations

  • Maeer's Mit Art Commerce Science College, Pune, Maharashtra, 412 105, India

Abstract

In this paper the generalized pseudo-differential type operator P(x,D), associated with the Bessel operator d2/dx2 + (1-4α2-4β2+8αβ)/4x2 is defined. The symbol class HmÏ,δ is introduced. It has been shown that the pseudo-differential type operator associated with a symbol belonging to this class is a continuous linear mapping of the Zemanian space Hα,β into itself. An integral representation of pseudo-differential type operator is obtained. Using Hankel type convolution,Lpμ,a-norm continuity of the pseudo-differential type operator is proved.

Keywords

Pseudo-Differential Opearator, Bessel Type Operator, Integral Representation, Hankel Type Transformation, Generalized Pseudo-Differential Operators.

Subject Discipline

Mathematical Sciences

Full Text:

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