An Application of Distributional Two Dimensional Fourier-Mellin Transform

V. D. Sharma, P. D. Dolas

Adjoint operator, Fourier Transform, Generalized function, Mellin Transform, Two Dimensional Fourier-Mellin Transform.

Integral transforms are linear continuous operators with their inverses, transforming a class of functions to another class of functions or sequences. They provide powerful operational methods for solving initial value problems and initial-boundary value problems for linear differential and integral equations. With ever greater demand for mathematical methods to provide a both theory and applications for science and engineering, the utility and interest of integral transforms seems more clearly established than ever. In spite of the fact that integral transforms have many mathematical and physical applications, their use is still predominant in advanced study and research. Keeping these features in mind in this paper we provide the solution of differential equation for the distributional two dimensional Fourier-Mellin transform of the type P(â‹€_(t,l,x,y)^* ) u(t,l,x,y)=f(t,l,x,y) and P(D_(t,l,x,y) )u(t,l,x,y)=f(t,l,x,y) using the differential operator â‹€_(t,l,x,y) and â‹€_(t,l,x,y)^*.

10.22161/ijaers/3.11.31