Index transforms associated with generalized hypergeometric functions
We deal with a class of integral transformations whose kernels contain the Clausenian hypergeometric function. These transforms are defined in terms of integrals with respect to their parameters. It involves as particular cases the familiar Olevskii and generalized Mehler-Fock transforms which are key tools in the methods of the mathematical
theory of elasticity. The main theorem of boundedness of these operators as a map in L_2 spaces is proved. Some examples of the Olevskii and Mehler-Fock type integrals are given.
Semyon Yakubovich (Departamento de Matemática Pura, Faculdade de Ciências da Universidade do Porto)
June 13, 2003