title: Approximation by entire functions on a countable set of continua. The inverse theorem
metadata.name: dc.contributor.author
metadata.value: Silvanovich, Olga V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Shirokov, Nikolay A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-02-16T19:19:07Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-02-16T19:19:07Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Silvanovich O.V., Shirokov N.A. Approximation by entire functions on a countable set of continua. The inverse theorem. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 4, pp. 600–607.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.405
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/35107
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The approximation theory contains many statements where the rate of approximation of a
  function by polynomials, rational functions and so on is measured with the help of a scale.
  The statements where some points on the relevant scale are associated with the smoothness
  of the approximated function are called direct theorems of the theory of approximation. The
  statements where the smoothness of the approximated function is derived from the points
  on the scale of approximation by polynomials, rational functions etc., are called inverse
  theorems of the theory of approximation. The class of functions is constructively discribed
  in terms of the rate of approximation by polynomials, rational functions etc., if the direct
  theorems correspond to the inverse theorems, i. e. the smoothness of the approximated
  function and the points on the scale of approximation have one-to-one correspondence for
  the class under consideration. The authors have stated earlier the direct theorem concerning
  approximation by entire functions of exponential type. We considered a set of functions
  defined on the countable set of mutually disjoint continua and found the rate of their
  approximation by those entire functions. The present paper contains the inverse theorem
  to the menthioned above direct one.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work of N.A. Shirokov was supported by the Russian Foundation for Basic Research (grant
  no. 20-01-00209).
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 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: inverse theorems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: theory of approximation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: entire functions of exponential type
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Hölder classes
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Approximation by entire functions on a countable set of continua. The inverse theorem
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 600-607.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/35107/1/600-607.pdf
resources.format: Adobe PDF
resources.size: 291,51 kB