Laguerre polynomial expansions in indefinite inner product spaces |
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Authors: | Allan M Krall |
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Affiliation: | McAllister Building, The Pennsylvania State University, University Park, Pennsylvania 16802 U.S.A. |
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Abstract: | When ?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. |
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