Ufa Mathematical Journal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Ufimsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Ufa Mathematical Journal, 2022, Volume 14, Issue 4, Pages 56–68
DOI: https://doi.org/10.13108/2022-14-4-56
(Mi ufa637)
 

Convergence of series of exponential monomials

A. S. Krivosheeva, O. A. Krivosheevab

a Institute of Mathematics, Ufa Federal Research Center, RAS, Chernyshevsky str. 112, 450008, Ufa, Russia
b Bashkir State University, Zaki Validi str. 32, 450076, Ufa, Russia
References:
Abstract: In the paper we study the convergence of series of exponential monomials, special cases of which are the series of exponentials, Dirichlet series and power series. We provide a description of the space of coefficients of series of exponential monomials converging in a given convex domain in the complex plane is described. Under a single natural restriction on the degrees of monomials, we provide a complete analogue of the Abel theorem for such series, which, in particular, implies results on the continued convergence of series of exponential monomials. We also obtain a complete analogue of the Cauchy-Hadamard theorem, in which we give a formula allowing to recover the convergence domain of these series by their coefficients. The obtained results include, as special cases, all previously known results related with the Abel and Cauchy-Hadamard theorems for exponential series, Dirichlet series and power series.
Keywords: exponential monomial, convex domain, Abel theorem, Cauchy-Hadamard theorem.
Funding agency Grant number
Contest «Young Russian Mathematics»
The research of the second author is supported by the contest «Youth Mathematics of Russia».
Received: 20.09.2022
Russian version:
Ufimskii Matematicheskii Zhurnal, 2022, Volume 14, Issue 4, Pages 60–72
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 30D10
Language: English
Original paper language: Russian
Citation: A. S. Krivosheev, O. A. Krivosheeva, “Convergence of series of exponential monomials”, Ufimsk. Mat. Zh., 14:4 (2022), 60–72; Ufa Math. J., 14:4 (2022), 56–68
Citation in format AMSBIB
\Bibitem{KriKri22}
\by A.~S.~Krivosheev, O.~A.~Krivosheeva
\paper Convergence of series of exponential monomials
\jour Ufimsk. Mat. Zh.
\yr 2022
\vol 14
\issue 4
\pages 60--72
\mathnet{http://mi.mathnet.ru/ufa637}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4516559}
\transl
\jour Ufa Math. J.
\yr 2022
\vol 14
\issue 4
\pages 56--68
\crossref{https://doi.org/10.13108/2022-14-4-56}
Linking options:
  • https://www.mathnet.ru/eng/ufa637
  • https://doi.org/10.13108/2022-14-4-56
  • https://www.mathnet.ru/eng/ufa/v14/i4/p60
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Уфимский математический журнал
    Statistics & downloads:
    Abstract page:61
    Russian version PDF:20
    English version PDF:26
    References:17
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024