Finite Gap Jacobi Matrices, I. The Isospectral Torus
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چکیده
Let e⊂ R be a finite union of disjoint closed intervals. In the study of orthogonal polynomials on the real line with measures whose essential support is e, a fundamental role is played by the isospectral torus. In this paper, we use a covering map formalism to define and study this isospectral torus. Our goal is to make a coherent presentation of properties and bounds for this special class as a tool for ourselves and others to study perturbations. One important result is the expression of Jost functions for the torus in terms of theta functions.
منابع مشابه
[ m at h . SP ] 3 1 Ju l 2 01 1 FINITE GAP JACOBI MATRICES , III . BEYOND THE SZEGŐ CLASS
Let e ⊂ R be a finite union of l + 1 disjoint closed intervals and denote by ωj the harmonic measure of the j leftmost bands. The frequency module for e is the set of all integral combinations of ω1, . . . , ωl. Let {ãn, b̃n}n=1 be a point in the isospectral torus for e and p̃n its orthogonal polynomials. Let {an, bn}n=1 be a half-line Jacobi matrix with an = ãn+δan, bn = b̃n+δbn. Suppose
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تاریخ انتشار 2008