Beiträge zur Theorie der Toeplitzschen Formen

Abstract

Das gesehieht mit Hilfe der folgenden Umformung yon ~ t., (C) : (27.) z.(c) = [c~_~-~_,+~]:-~ = Cn In der Tat, wenn ich seize, so gilt identisch -~o)(C -~0.,. (c -~_~)

F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach

“…Now we should take another mathematical interlude to state Szegö's theorem. This theorem determines how a Toeplitz determinant exponentially decays for large matrix size [23] and even finds a constant prefactor for the exponential decay [24,25]. The proof can be carried out using the Wiener-Hopf sum equation approach [20], but it would take too much space for us to repeat it here, and it is rife with many technical mathematical manipulations that would take us away from the physical phenomena we wish to discuss here.…”

“…Motivated by approaches that involve the integration over a coupling constant, we modify our time-dependent field by introducing a dependence on some new parameter that we denote by x 23) with the following limiting behavior…”

Trace formulas and a Borg‐type theorem for CMV operators with matrix‐valued coefficients

“…The relevance of CMV operators, more precisely, half-lattice CMV operators is derived from its intimate relationship with the trigonometric moment problem and hence with finite measures on the unit circle ∂ D. For a detailed account of the relationship of half-lattice CMV operators with orthogonal polynomials on the unit circle we refer to the monumental two-volume treatise by Simon [61] (see also [62], [63]) and the exhaustive bibliography therein. For classical results on orthogonal polynomials on the unit circle we refer, for instance, to [6], [29]- [31], [50], [69]- [71], [74], [75]. More recent references relevant to the spectral theoretic content of this paper are [18], [26]- [28], [39], [40], [43], [52], [59], [60].…”

Book Review: Schur\RM 's algorithm and several applications

“…The sources for the book by Bakonyi and Constantinescu are (1) Schur's study [33] of power series which represent analytic functions which are bounded by one in the unit disk and (2) Szegö's theory [34] of orthogonal polynomials on the unit circle. The subject has evolved through a series of generalizations which are formulated in the language of Hubert space operators, and today it is an active area with important engineering applications.…”

“…About the same time, Szegö [34] created his theory of orthogonal polynomials on the unit circle. Let w(6) be a nonnegative 2^-periodic measurable function on the real line with 1 T w(6)dd = 1.…”