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R. Pruckner, H. Woracek:
"Estimates for order of Nevanlinna matrices and a Berezanskii-type theorem";
in: "ASC Report 21/2016", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2016, ISBN: 978-3-902627-09-4, 1 - 27.

We give an upper estimate for the order of the entire functions in the Nevanlinna parameterisation 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 generalises a theorem of Yu.M.Berezanskii about spectral asymptotics of a Jacobi matrix (in the case that order is ≤ 1/2).

indeterminate moment problem, order of entire function, Berezanskii´s theorem, canonical system

http://www.asc.tuwien.ac.at/preprint/2016/asc21x2016.pdf