Laguerre polynomial expansions in indefinite inner product spaces

When ?j ? 1 < α < ?j, where j is a positive integer, the Laguerre polynomials {L_n^(α)}_{n = 0}^∞ form a complete orthogonal set in a nondegenerate inner product space H which is defined by employing an appropriate regularized linear functional on H^(j)[[0, ∞); x^{α + j}e^?x]. Expansions in terms of these Laguerre polynomials are exhibited. The Laguerre differential operator is shown to be self-adjoint with real, discrete, integer eigenvalues. Its spectral resolution and resolvent are exhibited and discussed.