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Funktsional. Anal. i Prilozhen., 2016, Volume 50, Issue 3, Pages 34–46 (Mi faa3244)  

This article is cited in 10 scientific papers (total in 10 papers)

Hyperquasipolynomials and their applications

V. A. Bykovskii

Far Eastern Branch of the Russian Academy of Sciences, Institute of Applied Mathematics Khabarovsk Division, Khabarovsk, Russia

Abstract: For a given nonzero entire function $g\colon\mathbb{C}\to\mathbb{C}$, we study the linear space $\mathcal{F}(g)$ of all entire functions $f$ such that
$$ f(z+w)g(z-w)=\varphi_1(z)\psi_1(w)+…+\varphi_n(z)\psi_n(w), $$
where $\varphi_1, \psi_1, …,\varphi_n,\psi_n\colon\mathbb{C}\to\mathbb{C}$. In the case of $g\equiv1$, the expansion characterizes quasipolynomials, that is, linear combinations of products of polynomials by exponential functions. (This is a theorem due to Levi-Civita.) As an application, all solutions of a functional equation in the theory of trilinear functional equations are obtained.

Keywords: quasipolynomial, Weierstrass sigma function, trilinear functional equation

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00203
Supported by RFBR grant no. 14-01-00203.


DOI: https://doi.org/10.4213/faa3244

Full text: PDF file (188 kB)
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English version:
Functional Analysis and Its Applications, 2016, 50:3, 193–203

Bibliographic databases:

Document Type: Article
UDC: 517.965+517.547.582
Received: 04.12.2015

Citation: V. A. Bykovskii, “Hyperquasipolynomials and their applications”, Funktsional. Anal. i Prilozhen., 50:3 (2016), 34–46; Funct. Anal. Appl., 50:3 (2016), 193–203

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Illarionov, “Functional Equations and Weierstrass Sigma-Functions”, Funct. Anal. Appl., 50:4 (2016), 281–290  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. A. Illarionov, “Reshenie funktsionalnogo uravneniya, svyazannogo s trilineinymi differentsialnymi operatorami”, Dalnevost. matem. zhurn., 16:2 (2016), 169–180  mathnet  elib
    3. M. D. Monina, “O range konechnogo nabora teta-funktsii”, Dalnevost. matem. zhurn., 16:2 (2016), 181–185  mathnet  elib
    4. A. A. Illarionov, M. A. Romanov, “O svyazi mezhdu giperellipticheskimi sistemami posledovatelnostei i funktsii”, Dalnevost. matem. zhurn., 17:2 (2017), 210–220  mathnet  elib
    5. A. A. Illarionov, “Solution of functional equations related to elliptic functions”, Proc. Steklov Inst. Math., 299 (2017), 96–108  mathnet  crossref  crossref  isi  elib
    6. V. A. Bykovskii, “O loranovosti posledovatelnosti Somos-4”, Dalnevost. matem. zhurn., 18:1 (2018), 18–22  mathnet
    7. A. A. Illarionov, M. A. Romanov, “Hyperquasipolynomials for the Theta-Function”, Funct. Anal. Appl., 52:3 (2018), 228–231  mathnet  crossref  crossref  isi  elib
    8. Bykovskii V.A., Monina M.D., “Integer Sequences Somos-4”, Dokl. Math., 98:1 (2018), 357–359  crossref  zmath  isi  scopus
    9. A. A. Illarionov, “O proizvedenii dvukh sigma-funktsii Veiershtrassa”, Issledovaniya po lineinym operatoram i teorii funktsii. 46, Zap. nauchn. sem. POMI, 467, POMI, SPb., 2018, 73–84  mathnet
    10. A. A. Illarionov, “O posledovatelnosti Somos-4”, Dalnevost. matem. zhurn., 18:2 (2018), 183–188  mathnet
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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