Integral operators related to generalized convolutions for Hankel transform

Abstract

The present research is devoted to integral transforms related to generalized convolutions, or polyconvolutions, for Hankel transform H _ν[f](x). Two polyconvolutions with the factorization properties

are considered in space . Existence conditions and boundary properties are found.

Watson’s type theorems for convolution transforms are proved. The integral transforms with unsymmetrical kernels are studied. Some applications to the corresponding class of convolution equations are given.

Keywords:

• Hankel transform
• convolution
• convolution transform
• Watson’s theorem
• integral equations

MSC :

• 44A05
• 44A35
• 45A05
• 45P05

Acknowledgements

The present investigation was partially supported by Federal Agency on Science and Innovations (grant 2006-RI-111.0/002/054).