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

This article is cited in 17 scientific papers (total in 17 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:

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

Citation in format AMSBIB
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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  mathscinet  isi  elib
    8. V. A. Bykovskii, M. D. Monina, “Integer sequences Somos-4”, Dokl. Math., 98:1 (2018), 357–359  mathnet  crossref  crossref  zmath  isi  elib  scopus
    9. A. A. Illarionov, “On products of Weierstrass sigma functions”, J. Math. Sci. (N. Y.), 243:6 (2019), 872–879  mathnet  crossref
    10. A. A. Illarionov, “O posledovatelnosti Somos-4”, Dalnevost. matem. zhurn., 18:2 (2018), 183–188  mathnet
    11. A. A. Illarionov, “Reshenie funktsionalnykh uravnenii, svyazannykh s ellipticheskimi funktsiyami. II”, Sib. elektron. matem. izv., 16 (2019), 481–492  mathnet  crossref
    12. A. A. Illarionov, “Hyperelliptic systems of sequences of rank 4”, Sb. Math., 210:9 (2019), 1259–1287  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    13. A. V. Ustinov, “An Elementary Approach to the Study of Somos Sequences”, Proc. Steklov Inst. Math., 305 (2019), 305–317  mathnet  crossref  crossref  mathscinet  isi  elib
    14. A. A. Illarionov, “Asimmetrichnye kriptosistemy i giperellipticheskie posledovatelnosti”, Dalnevost. matem. zhurn., 19:2 (2019), 185–196  mathnet
    15. A. A. Illarionov, N. V. Markova, “Reshenie funktsionalnykh uravnenii, svyazannykh s ellipticheskimi funktsiyami. III”, Dalnevost. matem. zhurn., 19:2 (2019), 197–205  mathnet
    16. A. A. Illarionov, “On a Multilinear Functional Equation”, Math. Notes, 107:1 (2020), 80–92  mathnet  crossref  crossref  mathscinet  isi  elib
    17. V. Ya. Prudnikov, “Zadacha o razdelenii peremennykh”, Dalnevost. matem. zhurn., 20:2 (2020), 227–233  mathnet  crossref
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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