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An Analog of the Hyperbolic Metric Generated by a Hilbert Space with the Schwarz–Pick Kernel. / Videnskii, I. V. .

In: Journal of Mathematical Sciences, Vol. 229, No. 5, 03.2018, p. 497-505.

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

Harvard

Videnskii, IV 2018, 'An Analog of the Hyperbolic Metric Generated by a Hilbert Space with the Schwarz–Pick Kernel', Journal of Mathematical Sciences, vol. 229, no. 5, pp. 497-505. https://doi.org/10.1007/s10958-018-3692-5

APA

Videnskii, I. V. (2018). An Analog of the Hyperbolic Metric Generated by a Hilbert Space with the Schwarz–Pick Kernel. Journal of Mathematical Sciences, 229(5), 497-505. https://doi.org/10.1007/s10958-018-3692-5

Vancouver

Videnskii IV. An Analog of the Hyperbolic Metric Generated by a Hilbert Space with the Schwarz–Pick Kernel. Journal of Mathematical Sciences. 2018 Mar;229(5):497-505. https://doi.org/10.1007/s10958-018-3692-5

Author

Videnskii, I. V. . / An Analog of the Hyperbolic Metric Generated by a Hilbert Space with the Schwarz–Pick Kernel. In: Journal of Mathematical Sciences. 2018 ; Vol. 229, No. 5. pp. 497-505.

BibTeX

@article{c48f8aa589eb4720af054d51511a4c33,
title = "An Analog of the Hyperbolic Metric Generated by a Hilbert Space with the Schwarz–Pick Kernel",
abstract = "It is proved that a Hilbert function space on a set X with the Schwarz–Pick kernel (this is a wider class than the class of Hilbert spaces with the Nevanlinna–Pick kernel) generates a metric on the set X which is an analog of the hyperbolic metric in the unit disk. For a sequence satisfying an abstract Blaschke condition, it is proved that the associated infinite Blaschke product converges uniformly on any fixed bounded set and in the strong operator topology of the multiplier space. Bibliography: 8 titles.",
keywords = "hiperbolic metric, multipliers, reproducing kernel",
author = "Videnskii, {I. V.}",
note = "Videnskii, I.V. An Analog of the Hyperbolic Metric Generated by a Hilbert Space with the Schwarz–Pick Kernel. J Math Sci 229, 497–505 (2018). https://doi.org/10.1007/s10958-018-3692-5",
year = "2018",
month = mar,
doi = "10.1007/s10958-018-3692-5",
language = "English",
volume = "229",
pages = "497--505",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "5",

}

RIS

TY - JOUR

T1 - An Analog of the Hyperbolic Metric Generated by a Hilbert Space with the Schwarz–Pick Kernel

AU - Videnskii, I. V.

N1 - Videnskii, I.V. An Analog of the Hyperbolic Metric Generated by a Hilbert Space with the Schwarz–Pick Kernel. J Math Sci 229, 497–505 (2018). https://doi.org/10.1007/s10958-018-3692-5

PY - 2018/3

Y1 - 2018/3

N2 - It is proved that a Hilbert function space on a set X with the Schwarz–Pick kernel (this is a wider class than the class of Hilbert spaces with the Nevanlinna–Pick kernel) generates a metric on the set X which is an analog of the hyperbolic metric in the unit disk. For a sequence satisfying an abstract Blaschke condition, it is proved that the associated infinite Blaschke product converges uniformly on any fixed bounded set and in the strong operator topology of the multiplier space. Bibliography: 8 titles.

AB - It is proved that a Hilbert function space on a set X with the Schwarz–Pick kernel (this is a wider class than the class of Hilbert spaces with the Nevanlinna–Pick kernel) generates a metric on the set X which is an analog of the hyperbolic metric in the unit disk. For a sequence satisfying an abstract Blaschke condition, it is proved that the associated infinite Blaschke product converges uniformly on any fixed bounded set and in the strong operator topology of the multiplier space. Bibliography: 8 titles.

KW - hiperbolic metric, multipliers, reproducing kernel

UR - http://www.scopus.com/inward/record.url?scp=85041528555&partnerID=8YFLogxK

U2 - 10.1007/s10958-018-3692-5

DO - 10.1007/s10958-018-3692-5

M3 - Article

VL - 229

SP - 497

EP - 505

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 15547343