B. N. Khabibullin, “Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions”, Sb. Math., 200:2 (2009), 283

Sbornik: Mathematics

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Mat. Sb.:
Year:
Volume:
Issue:
Page:
	Find

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

Sbornik: Mathematics, 2009, Volume 200, Issue 2, Pages 283–312
DOI: https://doi.org/10.1070/SM2009v200n02ABEH003996 (Mi sm3885)

This article is cited in 22 scientific papers (total in 22 papers)

Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions

B. N. Khabibullin^ab

^a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
^b Bashkir State University, Faculty of Mathematics

English version PDF (526 kB) Citations (22) Russian version article

References:

PDF

HTML

DOI: https://doi.org/10.1070/SM2009v200n02ABEH003996

Abstract: Let

Λ = {λ_{k}}

$\Lambda=\{\lambda_k\}$ be a sequence of points in the complex plane

$\mathbb C$ and

$f$ a non-trivial entire function of finite order

$\rho$ and finite type

$\sigma$ such that

$f=0$ on

$\Lambda$ . Upper bounds for functions such as the Weierstrass-Hadamard canonical product of order

$\rho$ constructed from the sequence

$\Lambda$ are obtained. Similar bounds for meromorphic functions are also derived. These results are used to estimate the radius of completeness of a system of exponentials in

$\mathbb C$ .
Bibliography: 26 titles.

Keywords: function, zero sequence, subharmonic function, radius of completeness, system of exponentials.

Received: 22.05.2007 and 12.08.2008

Bibliographic databases:

UDC: 517.547.2+517.538.2+517.581+517.574

MSC: 30C15, 30D15, 30D30

Language: English

Original paper language: Russian

Citation: B. N. Khabibullin, “Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions”, Sb. Math., 200:2 (2009), 283–312

Citation in format AMSBIB

\Bibitem{Kha09}

\by B.~N.~Khabibullin

\paper Zero sequences of holomorphic functions, representation of meromorphic functions. II.~Entire functions

\jour Sb. Math.

\yr 2009

\vol 200

\issue 2

\pages 283--312

\mathnet{http://mi.mathnet.ru/eng/sm3885}

\crossref{https://doi.org/10.1070/SM2009v200n02ABEH003996}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2503141}

\zmath{https://zbmath.org/?q=an:1167.30005}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2009SbMat.200..283K}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000266224500012}

\elib{https://elibrary.ru/item.asp?id=19066111}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67651061894}

Linking options:

https://www.mathnet.ru/eng/sm3885

https://doi.org/10.1070/SM2009v200n02ABEH003996

https://www.mathnet.ru/eng/sm/v200/i2/p129

Cycle of papers

Zero sequences of holomorphic functions, representation of meromorphic functions, and harmonic minorants
B. N. Khabibullin
Mat. Sb., 2007, 198:2, 121–160
Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions
B. N. Khabibullin
Mat. Sb., 2009, 200:2, 129–158

This publication is cited in the following 22 articles:

B. N. Khabibullin, “Distributions of zeros and masses of entire and subharmonic functions with restrictions on their growth along the strip”, Izv. Math., 88:1 (2024), 133–193
G. G. Braichev, V. B. Sherstyukov, “Uniqueness Theorem for Entire Functions of Exponential Type”, Lobachevskii J Math, 45:6 (2024), 2672
G. G. Braichev, “The Sylvester problem and uniqueness sets in classes of entire functions”, Journal of Mathematical Sciences, 286:1 (2024), 22–34
G. G. Braichev, “On the Connection between the Growth of Zeros and the Decrease of Taylor Coefficients of Entire Functions”, Math. Notes, 113:1 (2023), 27–38
B. N. Khabibullin, E. G. Kudasheva, A. E. Salimova, “Kriterii polnoty eksponentsialnoi sistemy v geometricheskikh terminakh shiriny v napravlenii”, Differentsialnye uravneniya i matematicheskaya fizika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 225, VINITI RAN, M., 2023, 150–159
A. M. Gaisin, B. E. Kanguzhin, A. A. Seitova, “Completeness of the exponential system on a segment of the real axis”, Eurasian Math. J., 13:2 (2022), 37–42
G. G. Braichev, O. V. Sherstyukova, “On least type of entire function with given subsequence of zeros”, Ufa Math. J., 14:3 (2022), 17–21
B. N. Khabibullin, E. B. Menshikova, “Preorders on Subharmonic Functions and Measures with Applications to the Distribution of Zeros of Holomorphic Functions”, Lobachevskii J Math, 43:3 (2022), 587
Khabibullin B.N. Menshikova E.B., “Balayage of Measures With Respect to Polynomials and Logarithmic Kernels on the Complex Plane”, Lobachevskii J. Math., 42:12 (2021), 2823–2833
A. F. Kuzhaev, “On the necessary and sufficient conditions for the measurability of a positive sequence”, Probl. anal. Issues Anal., 8(26):3 (2019), 63–72
V. B. Sherstyukov, “Asymptotic properties of entire functions with given laws of distribution of zeros”, J. Math. Sci. (N. Y.), 257:2 (2021), 246–272
G. G. Braichev, V. B. Sherstyukov, “Sharp bounds for asymptotic characteristics of growth of entire functions with zeros on given sets”, J. Math. Sci., 250:3 (2020), 419–453
V. B. Sherstyukov, “Minimal value for the type of an entire function of order $\rho\in(0,1)$ , whose zeros lie in an angle and have a prescribed density”, Ufa Math. J., 8:1 (2016), 108–120
G. G. Braichev, “Sharp Estimates of Types of Entire Functions with Zeros on Rays”, Math. Notes, 97:4 (2015), 510–520
G. G. Braichev, “The exact bounds of lower type magnitude for entire function of order $\rho\in(0,1)$ with zeros of prescribed average densities”, Ufa Math. J., 7:4 (2015), 32–57
F. S. Myshakov, “Analog teoremy Valirona—Goldberga pri ogranichenii na usrednennuyu schitayuschuyu funktsiyu mnozhestva kornei”, Anal Math, 41:3 (2015), 175
K. G. Malyutin, I. I. Kozlova, N. Sadik, “Canonical Functions of Admissible Measures in the Half-Plane”, Math. Notes, 96:3 (2014), 391–402
F. S. Myshakov, “An Analog of the Valiron–Goldberg Theorem under a Restriction Condition on the Averaged Counting Function of Zeros”, Math. Notes, 96:5 (2014), 831–835
G. G. Braichev, V. B. Sherstyukov, “On the Growth of Entire Functions with Discretely Measurable Zeros”, Math. Notes, 91:5 (2012), 630–644
G. G. Braichev, “The least type of an entire function of order $\rho\in(0,1)$ having positive zeros with prescribed averaged densities”, Sb. Math., 203:7 (2012), 950–975

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	1337
Russian version PDF:	431
English version PDF:	55
References:	156
First page:	25

Registration to the website

Logotypes