Pseudo-differential operators(p.d.o.)which originated as powerful tool in the study of partial differential equation,have now become an independent field of research. In fact, p.d.o are generalizations of partial differential operators. These operators have been defined on various functions and distribution spaces using various transformations. Pseudo-differential operators arise naturally in the solution of boundary value problemsfor partial differential equations. Hankel transformation is used in the solution of cylindrical boundary value problems. Therefore, the theory ofp.d.o involving Hankel transform will find applications in the characterizing solutions of cylindrical boundary value problems, which occur mostcommonly in nature.

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