Solving inverse scattering problem for a discrete Sturmâ€“Liouville operator with a rapidly decreasing potential one gets reflection coefficients sÂ± and invertible operators I + HsÂ± , where HsÂ± is theâ€¦ (More)

This work is in a stream (see e.g. [4], [8], [10], [11], [7]) initiated by a paper of Killip and Simon [9], an earlier paper [5] also should be mentioned here. Using methods of Functional Analysisâ€¦ (More)

We give an explicit parametrization of a set of almost periodic CMV matrices whose spectrum (is equal to the absolute continuous spectrum and) is a homogenous set E lying on the unit circle, forâ€¦ (More)

The main aim of this short paper is to advertize the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a newâ€¦ (More)

We prove that one-dimensional reflectionless SchrÃ¶dinger operators with spectrum a homogeneous set in the sense of Carleson, belonging to the class introduced by Sodin and Yuditskii, have purelyâ€¦ (More)

We present a new method that allows us to get a direct proof of the classical Bernstein asymptotics for the error of the best uniform polynomial approximation of |x| on two symmetric intervals. Note,â€¦ (More)

Abstract. Let E be a homogeneous compact set, for instance a Cantor set of positive length. Further let Ïƒ be a positive measure with supp(Ïƒ) = E. Under the condition that the absolutely continuousâ€¦ (More)

We generalize the Korkinâ€“Zolotarev theorem to the case of entire functions having the smallest L1 norm on a system of intervals E . If C \ E is a domain of Widom type with the Direct Cauchy Theorem,â€¦ (More)

We prove a partial result concerning the hard long standing problem on limit periodicity of the Jacobi matrix associated with the balanced measure on the Julia set of an expending polynomial. Besidesâ€¦ (More)