Generalized functions and Laguerre expansions

In this paper we study and characterize expansions of distributions in the Zemanian spaces, H μ and its dual H μ ′ ( μ ≥ - 1 2 ) with respect to Laguerre functions. We obtain as applications of this result, the kernel Theorem and a structure Theorem for H μ ′ . We also introduce a new algebra of generalized functions in the sense of J. F. Colombeau such that it satisfies interesting properties involving the Hankel transformation and Hankel convolution.