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In this work, we investigate the order of growth of the modulus of an arbitrary algebraic polynomials in the weighted Lebesgue space, where the contour and the weight functions have some singularities. In particular, we obtain new exact estimations for the growth of the modulus of orthogonal polynomials
In this work, we investigate the order of the growth of the modulus of orthogonal polynomials over a contour and also arbitrary algebraic polynomials in regions with corners in a weighted Lebesgue space, where the singularities of contour and the weight functions satisfy some condition.
In this present work, we continue studying the Nikol’skii and Bernstein–Walsh type estimations for complex algebraic polynomials in the bounded and unbounded regions bounded by asymptotically conformal curve.-
Keywords and phrases: Polynomials Nikol’skii inequalities Bernstein inequalities Conformal mapping Asymptotically conformal curve