Abstract. In this paper, we consider perturbations to a sequence of moments associated with an orthogonality linear functional that is represented by a positive measure supported in [−1, 1]. In particular, given a perturbation to such a measure on the real line, we analyze the perturbation obtained on the corresponding measure on the unit circle, when both measures are related through the Szeg ́́...

For Jacobi matrices with an 1⁄4 1þ ð 1Þan g; bn 1⁄4 ð 1Þbn g; we study bound states and the Szeg + o condition. We provide a new proof of Nevai’s result that if g4 2 ; the Szeg + o condition holds, which works also if one replaces ð 1Þ by cos ðmnÞ: We show that if a 1⁄4 0; ba0; and go1 2 ; the Szeg + o condition fails. We also show that if g 1⁄4 1; a and b are small enough (b þ 8a2o 1 24 will d...

Let e ⊂ R be a finite union of disjoint closed intervals. We study measures whose essential support is e and whose discrete eigenvalues obey a 1/2-power condition. We show that a Szeg˝ o condition is equivalent to lim sup a 1 · · · a n cap(e) n > 0 (this includes prior results of Widom and Peherstorfer–Yuditskii). Using Remling's extension of the Denisov–Rakhmanov theorem and an analysis of Jos...

Szeg˝ o's procedure to connect orthogonal polynomials on the unit circle and orthogonal polynomials on [−1, 1] is generalized to nonsymmetric measures. It generates the so-called semi-orthogonal functions on the linear space of Laurent polynomials Λ, and leads to a new orthogonality structure in the module Λ × Λ. This structure can be interpreted in terms of a 2 × 2 matrix measure on [−1, 1], a...

With s n (z) denoting the n-th partial sum of e z , the exact rate of convergence of the zeros of the normalized partial sums, s n (nz), to the Szeg} o curve D 0;1 was recently studied by Carpenter et al. (1991), where D 0;1 is deened by

A bstract We develop a new technique for computing class of four-point correlation functions heavy half-BPS operators in planar $$ \mathcal{N} N = 4 SYM theory which admit factorization into product two octagon form factors with an arbitrary bridge length. show that the can be expressed as Fredholm determinan...

Book review: Aniko Magashazi (2021). Singapore Globally Entangled. Lessons for Central Europe? K?szeg: Institute of Advanced Studies K?szeg (iASK), 310, ISBN 978-615-5742-15-6 Aniko Magashazi’s monograph provides an analysis that is embedded in a thorough and well-constructed discussion the major salient features Singapore. The novelty topic as evident today it was evaluated by author al...

Let p be a trigonometric polynomial, non-negative on the unit circle T. We say that a measure σ on T belongs to the polynomial Szeg˝ o class, if dσ(e iθ) = σ ′ ac (e iθ)dθ + dσ s (e iθ), σ s is singular, and 2π 0 p(e iθ) log σ ′ ac (e iθ) dθ > −∞ For the associated orthogonal polynomials {ϕ n }, we obtain pointwise asymp-totics inside the unit disc D. Then we show that these asymptotics hold in...

A new approach to the computation of the poles of a stable autoregressive system from the reeection coeecients is proposed. Equivalently, we compute the zeros of Szeg} o polynomials from the associated Schur parameters. The numerical method utilizes an eecient algorithm for computing the (unimodular) zeros of a unitary Hessenberg matrix; this step can be regarded as the computation of the poles...