Orthogonal series representations for generalized functions (Q1104516)

The paper contains a theory of expansion of certain Schwartz distributions with respect to series of orthonormal families of functions in weighted \(L^ p\) spaces, i.e. \(A_{L_ wp}\) spaces. Conditions for convergence of orthogonal series in these spaces have been found. Also their dual spaces have been studied and characterized. The results include theorems on expansions into series of orthogonal polynomials, such as Hermite, Laguerre, Legendre etc. polynomials. The theory has applications, for instance, in solving some differential equations in distribution spaces.