Nikolskii-type inequalities for generalized polynomials and zeros of orthogonal polynomials
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Generalized polynomials are defined as products of polynomials raised to positive real powers. The generalized degree can be defined in a natural way. Relying on Remez-type inequalities on the size of generalized polynomials, we estimate the supremum norm of a generalized polynomial by its weighted L1 norm. Based on such Nikolskii-type inequalities we give sharp upper bounds for the distance of the consecutive zeros of orthogonal polynomials associated with weight functions from rather wide classes. The estimates contain some old results as special cases. © 1991.
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