Stability of the derivative of a canonical product

Tools

Langer, Matthias and Woracek, Harald (2014) Stability of the derivative of a canonical product. Complex Analysis and Operator Theory, 8 (6). pp. 1183-1224. ISSN 1661-8254 (https://doi.org/10.1007/s11785-013-0315-5)

[thumbnail of Langer-Woracek-CAOT2014-stability-of-the-derivative-of-a-canonical-product-aam]
Preview
 PDF. Filename: Langer_Woracek_CAOT2014_stability_of_the_derivative_of_a_canonical_product_aam.pdf
Accepted Author Manuscript
Download (396kB)| Preview

Abstract

With each sequence α=(αn)n∈N of pairwise distinct and non-zero points which are such that the canonical product   Pα(z):=limr→∞∏∣αn∣≤r(1−z/αn) converges, the sequence   α′:=(Pα'(αn))n∈N is associated. We give conditions on the difference β−α of two sequences which ensure that β' and α' are comparable in the sense that   ∃c,C>0: c|α'n|≤|β'n|≤C|α'n|,  n∈N. The values α'n play an important role in various contexts. As a selection of applications we present: an inverse spectral problem, a class of entire functions and a continuation problem.

ORCID iDs

Langer, Matthias ORCID logoORCID: https://orcid.org/0000-0001-8813-7914 and Woracek, Harald;
CORE (COnnecting REpositories)