Stability of the derivative of a canonical product

Matthias Langer, Harald Woracek

Research output: Contribution to journalArticle

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'n))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.

LanguageEnglish
Pages1183-1224
Number of pages42
JournalComplex Analysis and Operator Theory
Volume8
Issue number6
Early online date11 Jul 2013
DOIs
Publication statusPublished - Aug 2014

Fingerprint

Derivatives
Derivative
Inverse Spectral Problem
Entire Function
Continuation
Pairwise
Distinct
Converge
Context
Class

Keywords

  • canonical product
  • perturbation of zeros
  • inverse spectral problem
  • Krein class
  • positive definite function

Cite this

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Stability of the derivative of a canonical product. / Langer, Matthias; Woracek, Harald.

In: Complex Analysis and Operator Theory, Vol. 8, No. 6, 08.2014, p. 1183-1224.

Research output: Contribution to journalArticle

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