ASYNPTOTIC PROPERTIES OF ORTHOGONAL POLYNOMIALS AND THEIR DERIVATIVES

Abstract

The asymptotic properties of the multinomials being orthogonal on the circle and their derivatives of the natural order are investigated. For orthogonal multinomial on the circle the asymptotics in Segeau form being even inner arc not containing the special points of the distribution density has been proved at minimal limitations for the smoothness of the later. For wide classes with special features, the flow evaluations of the Segeau function module, weight analogies of the Markov, Bernstein and Nikolski inequalities and sometimes also the even asymptotic representations of the orthogonal multinomials on the circle and their derivatives have been specified. As a consequence the results about asymptotics of the orthogonal trigonometric polynomials and multinomials being orthogonal on the line (specifically, generalized Jacobian multinomials) have been obtained.Available from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio