title: Power series of several variables with condition of logarithmical convexity
metadata.name: dc.contributor.author
metadata.value: Zheleznyak, Alexandr V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-05-04T19:05:41Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-05-04T19:05:41Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zheleznyak А.V. Power series of several variables with condition of logarithmical convexity. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 1, pp. 49–62.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.105
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/28433
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We obtain a new version of Hardy theorem about power series of several variables reciprocal
  to the power series with positive coefficients. We prove that if the sequence
  {as} = as1,s2,...,sn, ||s|| ≥ K satisfies condition of logarithmically convexity and the first
  coefficient a0 is sufficiently large then reciprocal power series has only negative coefficients
  {bs} = bs1,s2,...,sn, except b0,0,...,0 for any K. The classical Hardy theorem corresponds to
  the case K = 0, n = 1. 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.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 8 (66); 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: Power series of several variables with condition of logarithmical convexity
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 49-62.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/28433/1/49-62.pdf
resources.format: Adobe PDF
resources.size: 321,22 kB