On K_μ Transformation of Distributions

Abstract

In this paper the integral K–_μ transformation, also known as Meijer transformation, is defined on new spaces of generalized functions. We use a procedure based on adjoint operators. The Mellin integral transformation plays an important role in our study and it allows to show that the classical K_μ transformation is an isomorphism between certain Fréchet function spaces introduced herein. We establish connections between our generalized K_μ transformation and thewell–known K_μ transform studied by A.H. Zemanian

Keywords:

• Integral K_μ transformation
• Bessel function
• Mellin transformation
• generalized functions

AMS(MOS)::

• 46F12