Abstract
A class of orthonormal polynomials with asymptotically N -periodic recurrence coefficients (APN class) is studied. These polynomials have an essential spectral measure supported on at most N disjoint intervals. By the same approach, for polynomials of class APN, the following two problems are solved: to extend the trace formula and to find an asymptotics of Turán’s determinant for polynomials orthogonal on several intervals.
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