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UPA Perpustakaan Universitas Jember

Bounds on Order of Indeterminate Moment Sequences

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We investigate the order ρ of the four entire functions in the Nevanlinna
matrix of an indeterminate Hamburger moment sequence. We give an upper estimate
for ρ which is explicit in terms of the parameters of the canonical system associated
with the moment sequence via its three-term recurrence. Under a weak regularity
assumption, this estimate coincides with a lower estimate, and hence ρ becomes computable. Dropping the regularity assumption leads to examples where upper and lower
bounds do not coincide and differ from the order. In particular, we provide examples
for which the order is different from its lower estimate due to M.S. Livšic.

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