Analytic properties of telescoping series derived from the zeros of the polynomial components

TitleAnalytic properties of telescoping series derived from the zeros of the polynomial components
Publication TypeJournal Article
Year of Publication2019
AuthorsBlatt, H-P, .Nguyen, E
JournalDolomites Research Notes on Approximation
Volume12
IssueSpecial_Issue
Pagination1-9
Date Published10/2019
PublisherPadova University Press
Place PublishedPadova, IT
ISSN Number2035-6803
Keywordsanalytic continuation, Bernstein- Walsh theorem, polynomial approximation, telescoping series
Abstract

 

Telescoping polynomial series with specified restrictions on the zeros of the polynomial components turn out to be entire functions. Applied to polynomial Lp-approximation, 1 < p ≤ ∞, on a compact set E, we obtain a converse theorem based only on the location of the zeros of the difference of consecutive polynomials and the asymptotic behavior of the zeros of the polynomials. In contrast to the Bernstein- Walsh theorem, no information about the asymptotic behavior of the error of approximation is needed.