Laguerre polynomial expansions in indefinite inner product spaces

AbstractWhen −j − 1 < α < −j, where j is a positive integer, the Laguerre polynomials {Ln(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, ∞); xα + je−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