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

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.

Blatt H., Nguyen E., Blatt H. P. (2019) "Analytic properties of telescoping series derived from the zeros of the polynomial components " Dolomites Research Notes on Approximation, 12(Special_Issue), 1-9. DOI: 10.14658/PUPJ-DRNA-2019-Special_Issue-2  
Year of Publication
2019
Journal
Dolomites Research Notes on Approximation
Volume
12
Issue Number
Special_Issue
Start Page
1
Last Page
9
Date Published
10/2019
ISSN Number
2035-6803
Serial Article Number
2
DOI
10.14658/PUPJ-DRNA-2019-Special_Issue-2
Issue
Section
SpecialIssue