On the Trigonometric Moment Problem

Abstract

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Weyl–Titchmarsh theory for CMV operators associated with orthogonal polynomials on the unit circle

“…For a detailed account of the relationship of U +,0 with orthogonal polynomials on the unit circle we refer to the monumental two-volume treatise by Simon [33] (see also [32] and [34] for a description of some of the principal results in [33]) and the exhaustive bibliography therein. For classical results on orthogonal polynomials on the unit circle we refer, for instance, to [3,[15][16][17]23,25,[35][36][37][38][39][40]. More recent references relevant to the spectral theoretic content of this paper are [12][13][14]20,22,26,30,31].…”

On a spectral theorem in paraorthogonality theory

“…We recall that the solution of the trigonometric moment problem is always unique [Geronimus 1946;Jones et al 1989]. The associated orthonormal polynomials are given by…”

Orthogonal Polynomials

“…The special case = −1 goes back to Verblunsky [35] and Geronimus [12], and are called the second kind polynomials, denoted n (z). The following goes back to Verblunsky [35].…”