Loading [MathJax]/jax/output/SVG/config.js
Journal of Siberian Federal University. Mathematics & Physics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



J. Sib. Fed. Univ. Math. Phys.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Journal of Siberian Federal University. Mathematics & Physics, 2023, Volume 16, Issue 6, Pages 758–772 (Mi jsfu1122)  

On the non-standard interpolations in $\mathbb{C}^n$ and combinatorial coefficients for Weil polyhedra

Matvey E. Durakova, Roman V. Ulvertba, August K. Tsikha

a Siberian Federal University, Krasnoyarsk, Russian Federation
b Reshetnev Siberian State University of Science and Technology, Krasnoyarsk, Russian Federation
References:
Abstract: Multidimensional non-standard interpolation has been recently presented in an article by D. Alpay and A. Yger. We are talking about algebraic interpolation where discrete roots of a system of polynomial equations serve as nodes. With the help of the Grothendieck residue duality, the problem of describing the desired interpolation space of functions is reduced to solving the affine-bilinear equation. To implement this reduction, algorithms for calculating local Grothendieck residues or their sums are required. In a fairly general situation, the calculation of these residues is based on the well-known Gelfond–Khovanskii formula. This article provides examples of calculating local residues or their sums. In 2-dimensional case we generalise the Gelfond–Khovanskii formula for Newton polyhedra that are not in the unfolded position. This is done using the concept of an amoeba of an algebraic set and the notion of an homological resolvent for the boundary of Weil polyhedron.
Keywords: Grothendieck residue, interpolation, amoeba, Homological resolvent.
Funding agency Grant number
Russian Science Foundation 20-11-20117
The investigation was supported by the Russian Science Foundation, grant no. 20-11-20117.
Received: 10.08.2023
Received in revised form: 27.09.2023
Accepted: 24.10.2023
Bibliographic databases:
Document Type: Article
UDC: УДК~517.55
Language: English
Citation: Matvey E. Durakov, Roman V. Ulvert, August K. Tsikh, “On the non-standard interpolations in $\mathbb{C}^n$ and combinatorial coefficients for Weil polyhedra”, J. Sib. Fed. Univ. Math. Phys., 16:6 (2023), 758–772
Citation in format AMSBIB
\Bibitem{DurUlvTsi23}
\by Matvey~E.~Durakov, Roman~V.~Ulvert, August~K.~Tsikh
\paper On the non-standard interpolations in $\mathbb{C}^n$ and combinatorial coefficients for Weil polyhedra
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2023
\vol 16
\issue 6
\pages 758--772
\mathnet{http://mi.mathnet.ru/jsfu1122}
\edn{https://elibrary.ru/HRVUPS}
Linking options:
  • https://www.mathnet.ru/eng/jsfu1122
  • https://www.mathnet.ru/eng/jsfu/v16/i6/p758
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал Сибирского федерального университета. Серия "Математика и физика"
    Statistics & downloads:
    Abstract page:96
    Full-text PDF :37
    References:22
     
      Contact us:
    math-net2025_05@mi-ras.ru
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025