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Estimates for the order of Nevanlinna matrices and a Berezanskii-type theorem
Published online by Cambridge University Press: 26 January 2019
Abstract
We give an upper estimate for the order of the entire functions in the Nevanlinna parameterization of the solutions of an indeterminate Hamburger moment problem. Under a regularity condition this estimate becomes explicit and takes the form of a convergence exponent. Proofs are based on transformations of canonical systems and I.S.Kac' formula for the spectral asymptotics of a string. Combining with a lower estimate from previous work, we obtain a class of moment problems for which order can be computed. This generalizes a theorem of Yu.M.Berezanskii about spectral asymptotics of a Jacobi matrix (in the case that order is ⩽ 1/2).
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 6 , December 2019 , pp. 1637 - 1661
- Copyright
- Copyright © Royal Society of Edinburgh 2019