Some Classes of Watson Transforms and Related Integral Equations for Generalized Functions
Boele L. J. Braaksma, A. Schuitman · SIAM Journal on Mathematical Analysis · 1976
Spaces of testing functions which are isomorphically mapped onto one another by the Mellin and the inverse Mellin transform are used to prove that certain spaces are also mapped isomorphically onto one another by the so-called Watson transform. Then Watson transforms for generalized functions are defined. Applications on Hankel transforms, fractional integrals and integral equations of Love involving hypergeometric functions and of Fox involving H-functions are given. Furthermore, dual integral equations for generalized functions with Hankel transforms and H-functions are treated.