title: Extremal polynomials connected with Zolotarev polynomials
metadata.name: dc.contributor.author
metadata.value: Agafonova, Irina V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Malozemov, Vassili N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-04-10T12:09:42Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-04-10T12:09:42Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Agafonova I.V., Malozemov V.N. Extremal polynomials connected with Zolotarev polynomials. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 1, pp. 3–14.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.101
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17323
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Let two points a and b be given on the real axis, located to the right and left of the segment
  [−1, 1] respectively. The extremal problem is posed: find an algebraic polynomial of n-th
  degree, which at the point a takes value A, on the segment [−1, 1] does not exceed M in
  modulus and takes the largest possible value at b. This problem is related to the second
  problem of Zolotarev. In the article the set of values of the parameter A for which this
  problem has a unique solution is indicated, and an alternance characteristic of this solution
  is given. The behavior of the solution with respect to the parameter A is studied. It turns
  out that for some A the solution can be obtained with the help of the Chebyshev polynomial,
  while for all other admissible A   with the help of the Zolotarev polynomial.
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: extremal properties of polynomials
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: alternance
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Chebyshev polynomials
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Zolotarev polynomials
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Extremal polynomials connected with Zolotarev polynomials
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 3-14.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17323/1/3-14.pdf
resources.format: Adobe PDF
resources.size: 315,25 kB