Let σ be a positive measure whose support is an interval E plus a denumerable set of mass points which accumulate at the boundary points of E only. Under the assumptions that the mass points satisfy… (More)

The algebraic structure of V.P. Potapov's Fundamental Matrix Inequality (FMI) is discussed and its interpolation meaning is analyzed. Functional model spaces are involved. A general Abstract… (More)

In 1877, E. I. Zolotarev [19, 2] found an explicit expression, in terms of elliptic functions, of the rational function of given degree m which is uniformly closest to sgn (x) on the union of two… (More)

We describe polynomials of the best uniform approximation to sgn(x) on the union of two intervals [−A,−1] ∪ [1, B] in terms of special conformal mappings. This permits us to find the exact asymptotic… (More)

In 1969 Harold Widom published his seminal paper (Widom, 1969) which gave a complete description of orthogonal and Chebyshev polynomials on a system of smooth Jordan curves. When there were Jordan… (More)

1. Ergodic finite difference operators and associated Riemann surfaces The standard (three–diagonal) finite–band Jacobi matrices [2, 4] can be defined as almost periodic or even ergodic Jacobi… (More)

The starting point of our research concerned the problem of Bellisard about almost periodicity of a wide and natural class of Jacobi matrices with singular continuous spectrum, which appear naturally… (More)

First we give here a simple proof of a remarkable result of Videnskii and Shirokov: let B be a Blaschke product with n zeros, then there exists an outer function φ, φ(0) = 1, such that (Bφ) ′ ≤ Cn,… (More)

In recent works we considered an asymptotic problem for orthogonal polynomials when a Szegö measure on the unit circumference is perturbed by an arbitrary Blaschke sequence of point masses outside… (More)

We consider Nehari's problem in the case of non-uniqueness of solution. The solution set is then parametrized by the unit ball of H ∞ by means of so-called regular generators — bounded holomorphic… (More)