Weighted Remez- and Nikolskii-Type Inequalities on a Quasismooth Curve
نویسندگان
چکیده
منابع مشابه
Remez-, Nikolskii-, and Markov-Type Inequalities for Generalized Nonnegative Polynomials with Restricted Zeros
Generalized nonnegative polynomials were studied in a sequence of recent papers [4], [6], [7], [8], and [9]. A number of well-known inequalities in approximation theory were extended to them, by utilizing the generalized degree in place of the ordinary one. Our motivation was to find tools to examine systems of orthogonal polynomials simultaneously, associated with generalized Jacobi, or at lea...
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The classical Remez inequality ([33]) bounds the maximum of the absolute value of a real polynomial P of degree d on [−1, 1] through the maximum of its absolute value on any subset Z ⊂ [−1, 1] of positive Lebesgue measure. Extensions to several variables and to certain sets of Lebesgue measure zero, massive in a much weaker sense, are available (see, e.g., [14, 39, 8]). Still, given a subset Z ...
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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 alge...
متن کاملMüntz Spaces and Remez Inequalities
Two relatively long-standing conjectures concerning Müntz polynomials are resolved. The central tool is a bounded Remez type inequality for non-dense Müntz spaces.
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ژورنال
عنوان ژورنال: Computational Methods and Function Theory
سال: 2018
ISSN: 1617-9447,2195-3724
DOI: 10.1007/s40315-018-0234-6