title: On the constants in the inverse theorems for the first derivative
metadata.name: dc.contributor.author
metadata.value: Vinogradov, Oleg L.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-02-16T17:36:38Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-02-16T17:36:38Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vinogradov O. L. On the constants in the inverse theorems for the first derivative. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 4, pp. 559–571.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.401
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/35103
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The known proofs of the inverse theorems of the theory of approximation by trigonometric
  polynomials and by functions of exponential type are based on the idea of S.N.Bernstein to
  expand a function in a series containing its functions of best approximation. In this paper,
  a new method to establish the inverse theorems is introduced. We establish simple identities
  that immediately imply the inverse theorems mentioned and, moreover, with better
  constants. This method can be applied to derivatives of arbitrary order (not necessarily
  an integer one) and (with certain modifications) to estimates of some other functionals in
  terms of best approximations. In this paper, the case of the first derivative of a function
  itself and of its trigonometrically conjugate is considered.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work is supported by the Russian Science Foundation (grant no. 18-11-00055).
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: conjugate function
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the constants in the inverse theorems for the first derivative
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 559-571.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/35103/1/559-571.pdf
resources.format: Adobe PDF
resources.size: 319,06 kB