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Bounds on order of indeterminate moment sequences. / Pruckner, Raphael; Romanov, Roman; Woracek, Harald.

In: Constructive Approximation, Vol. 46, 2017, p. 199-225.

Research output: Contribution to journal › Article › peer-review

Harvard

Pruckner, R, Romanov, R & Woracek, H 2017, 'Bounds on order of indeterminate moment sequences', Constructive Approximation, vol. 46, pp. 199-225. https://doi.org/10.1007/s00365-016-9351-5

APA

Pruckner, R., Romanov, R., & Woracek, H. (2017). Bounds on order of indeterminate moment sequences. Constructive Approximation, 46, 199-225. https://doi.org/10.1007/s00365-016-9351-5

Vancouver

Pruckner R, Romanov R, Woracek H. Bounds on order of indeterminate moment sequences. Constructive Approximation. 2017;46:199-225. https://doi.org/10.1007/s00365-016-9351-5

Author

Pruckner, Raphael ; Romanov, Roman ; Woracek, Harald. / Bounds on order of indeterminate moment sequences. In: Constructive Approximation. 2017 ; Vol. 46. pp. 199-225.

BibTeX

@article{fa21771183f549c989c5cbd1e7e49510,
title = "Bounds on order of indeterminate moment sequences",
abstract = "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 com- putable. 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. Liv{\v s}ic.",
keywords = "Indeterminate moment problem · Canonical system · Order of entirefunction · Asymptotic of eigenvalues",
author = "Raphael Pruckner and Roman Romanov and Harald Woracek",
year = "2017",
doi = "10.1007/s00365-016-9351-5",
language = "English",
volume = "46",
pages = "199--225",
journal = "Constructive Approximation",
issn = "0176-4276",
publisher = "Springer Nature",

}

RIS

TY - JOUR

T1 - Bounds on order of indeterminate moment sequences

AU - Pruckner, Raphael

AU - Romanov, Roman

AU - Woracek, Harald

PY - 2017

Y1 - 2017

N2 - 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 com- putable. 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.

AB - 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 com- putable. 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.

KW - Indeterminate moment problem · Canonical system · Order of entirefunction · Asymptotic of eigenvalues

U2 - 10.1007/s00365-016-9351-5

DO - 10.1007/s00365-016-9351-5

M3 - Article

VL - 46

SP - 199

EP - 225

JO - Constructive Approximation

JF - Constructive Approximation

SN - 0176-4276

ER -

ID: 7736720