Title

On the size of polynomials with curved majorant

Abstract

Let Cn(φ) denote all polynomials of degree n majorized by a positive C2 function φ on [-1,1], n = 0, 1, 2, … . We establish that for every r ∈ (0, 1), there is an integer N(r, φ) > 0, such that, for all n ≥ N(r, φ), the polynomials in Cn(φ) could be as large as φ on [-r, r], i.e., [formula] for all x ∈ [-r, r] and n ≥ N(r, φ). This is related to a result of Newman and Rivlin [6]. © 1994 Academic Press, Inc.

Publication Date

1-1-1994

Publication Title

Journal of Approximation Theory

Volume

76

Issue

1

Number of Pages

93-106

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1006/jath.1994.1007

Socpus ID

43949154232 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/43949154232

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