title: Multiplicative property of series used in the Nevanlinna - Pick problem
metadata.name: dc.contributor.author
metadata.value: Zheleznyak, Аlexander V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-04-14T11:04:49Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-04-14T11:04:49Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zheleznyak А.V. Multiplicative property of series used in the Nevanlinna - Pick problem. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 1, pp. 37–45.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.104
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/36152
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In the paper we obtained substantially new sufficient condition for negativity of coefficients of power series inverse to series with positive ones. It has been proved that element-wise product of power series retains this property. In particular, it gives rise to generalization of the classical Hardy theorem about power series. These results are generalized for cases of series with multiple variables. Such results are useful in Nevanlinna – Pick theory. For example, if function k(x, y) can be represented as power series Pn≥0 an(x¯y)n, an > 0, and reciprocal function 1/k(x, y) can be represented as power series Pn≥0 bn(x¯y)n such that bn < 0, n > 0, then k(x, y) is a reproducing kernel function for some Hilbert space of analytic functions in the unit disc D with Nevanlinna – Pick property. The reproducing kernel 1/(1 − x¯y) of the classical Hardy space H2(D) is a prime example for our theorems.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 9; Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: power series
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Nevanlinna - Pick kernels
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: logarithmical convexity
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Multiplicative property of series used in the Nevanlinna - Pick problem
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 37-45.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/36152/1/37-45.pdf
resources.format: Adobe PDF
resources.size: 290,55 kB