Remez‐Type Inequalities on the Size of Generalized 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. A number of classical inequalities holding for polynomials can be extended for generalized polynomials utilizing the generalized degree in place of the ordinary one. Remez established a sharp upper bound for the maximum modulus on [- 1,1] of algebraic polynomials of degree at most n if the measure of the subset of [-1,1], where the modulus of the polynomial is at most 1, is known. In this paper a numerical version of the Remez inequality is extended for generalized complex algebraic polynomials and its trigonometric and pointwise algebraic analogues are discussed. The results are new even for ordinary polynomials. © 1992 Oxford University Press.
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