Abstract (EN):
We deduce a product formula for the Whittaker function W-kappa,W-mu whose kernel does not depend on the second parameter. Making use of this formula, we define the positivity-preserving convolution operator associated with the index Whittaker transform, which is seen to be a direct generalization of the Kontorovich-Lebedev convolution. The mapping properties of this convolution operator are investigated; in particular, a Banach algebra property is established and then applied to yield an analogue of the Wiener-Levy theorem for the index Whittaker transform. We show how our results can be used to prove the existence of a unique solution for a class of convolution-type integral equations.
Idioma:
Inglês
Tipo (Avaliação Docente):
Científica
Nº de páginas:
27