The left-definite Legendre type boundary problem
In this paper, we show that the spaceC2[−1, 1] is dense inH, from which it follows that the spectrum of the self-adjoint left-definite operatorS k [·] associated withM k [·] is a purely point spectrum and consists only of the eigenvaluesλ n . Comparisons betweenS k [·] and the associated right-definite operatorT k [·] are made. This work extends earlier work of Everitt, Krall, Littlejohn, and Williams.
AMS classification33A65 34B20
Key words and phrasesOrthogonal polynomials Singular differential equation Legendre type boundary problem Weighted Sobolev space
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