title: Power series of one variable with condition of logarithmical convexity
metadata.name: dc.contributor.author
metadata.value: Zheleznyak, Alexandr V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-04-10T12:20:22Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-04-10T12:20:22Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zheleznyak A.V. Power series of one variable with condition of logarithmical convexity. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 1, pp. 28–38.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.103
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17325
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We obtain a new version of Hardy theorem about power series reciprocal to the power series
  with positive coefficients. We prove that if the sequence {an}, n   K is logarithmically
  convex, then reciprocal power series has only negative coefficients bn, n > 0 for any K if the
  first coefficient a0 is sufficiently large. The classical Hardy theorem corresponds to the case
  K = 0. 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. In addition, we get new estimates on growth
  of analytic functions reciprocal to analytic functions with positive Taylor coefficients.
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 7 (65); 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 one variable with condition of logarithmical convexity
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 28-38.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17325/1/28-38.pdf
resources.format: Adobe PDF
resources.size: 309,49 kB