SPECTRAL ANALYSIS FOR THE EXCEPTIONAL Xm-JACOBI EQUATION
نویسنده
چکیده
We provide the mathematical foundation for the Xm-Jacobi spectral theory. Namely, we present a self-adjoint operator associated to the differential expression with the exceptional Xm-Jacobi orthogonal polynomials as eigenfunctions. This proves that those polynomials are indeed eigenfunctions of the self-adjoint operator (rather than just formal eigenfunctions). Further, we prove the completeness of the exceptional Xm-Jacobi orthogonal polynomials (of degrees m, m + 1, m + 2, . . . ) in the Lebesgue-Hilbert space with the appropriate weight. In particular, the self-adjoint operator has no other spectrum.
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