Stability of the derivative of a canonical product

Matthias Langer, Harald Woracek

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With each sequence α=(αn)n∈N of pairwise distinct and non-zero points which are such that the canonical product
converges, the sequence
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.

Original languageEnglish
Pages (from-to)1183-1224
Number of pages42
JournalComplex Analysis and Operator Theory
Issue number6
Early online date11 Jul 2013
Publication statusPublished - Aug 2014


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


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