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