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Mat. Sb., 2007, Volume 198, Number 12, Pages 37–46 (Mi msb3858)  

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

A majoration principle for meromorphic functions

V. N. Dubinin, S. I. Kalmykov

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: A new majoration principle for meromorphic functions with prescribed poles is considered. Covering and distortion results for rational functions and polynomials are consequences of this principle. In particular, a simple proof of a Bernstein-type inequality for rational functions on several intervals is presented.
Bibliography: 17 titles.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm3858

Full text: PDF file (460 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2007, 198:12, 1737–1745

Bibliographic databases:

UDC: 517.547.24+517.535
MSC: Primary 26C15, 30D30, 41A17; Secondary 30C10
Received: 16.04.2007 and 28.06.2007

Citation: V. N. Dubinin, S. I. Kalmykov, “A majoration principle for meromorphic functions”, Mat. Sb., 198:12 (2007), 37–46; Sb. Math., 198:12 (2007), 1737–1745

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. L. Lukashov, “Additions to the Principle of Harmonic Nevanlinna Measure”, Math. Notes, 84:4 (2008), 589–591  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. N. Dubinin, “Majorization Principles for Meromorphic Functions”, Math. Notes, 84:6 (2008), 751–755  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. S. I. Kalmykov, “Majoration principles and some inequalities for polynomials and rational functions with prescribed poles”, J. Math. Sci. (N. Y.), 157:4 (2009), 623–631  mathnet  crossref  zmath
    4. V. N. Dubinin, D. B. Karp, V. A. Shlyk, “Izbrannye zadachi geometricheskoi teorii funktsii i teorii potentsiala”, Dalnevost. matem. zhurn., 8:1 (2008), 46–95  mathnet  elib
    5. V. V. Vasin, V. N. Dubinin, V. G. Romanov, “Itogovyi nauchnyi otchet po mezhdistsiplinarnomu integratsionnomu proektu SO RAN: “Razrabotka teorii i vychislitelnoi tekhnologii resheniya obratnykh i ekstremalnykh zadach s prilozheniem v matematicheskoi fizike i gravimagnitorazvedke””, Sib. elektron. matem. izv., 5 (2008), 427–439  mathnet  elib
    6. V. N. Dubinin, “Emkosti kondensatorov i printsipy mazhoratsii v geometricheskoi teorii funktsii kompleksnogo peremennogo [Itogovyi nauchnyi otchet po mezhdistsiplinarnomu integratsionnomu proektu SO RAN: “Razrabotka teorii i vychislitelnoi tekhnologii resheniya obratnykh i ekstremalnykh zadach s prilozheniem v matematicheskoi fizike i gravimagnitorazvedke”]”, Sib. elektron. matem. izv., 5 (2008), 465–482  mathnet  mathscinet
    7. S. I. Kalmykov, “Polynomials with curved majorants on two segments”, Russian Math. (Iz. VUZ), 53:10 (2009), 64–67  mathnet  crossref  mathscinet  zmath  elib
    8. S. I. Kalmykov, “Covering theorems for polynomials with curved majorants on two segments”, J. Math. Sci. (N. Y.), 178:2 (2011), 170–177  mathnet  crossref
    9. V. N. Dubinin, S. I. Kalmukov, “On polynomials with constraints on circular arcs”, J. Math. Sci. (N. Y.), 184:6 (2012), 703–708  mathnet  crossref
    10. V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    11. S. I. Kalmykov, “On polynomials and rational functions normalized on the circular arcs”, J. Math. Sci. (N. Y.), 200:5 (2014), 577–585  mathnet  crossref
    12. Akturk M.A., Lukashov A., “Weighted Analogues of Bernstein-Type Inequalities on Several Intervals”, J. Inequal. Appl., 2013, 487  crossref  mathscinet  zmath  isi  elib  scopus
    13. A. V. Olesov, “Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials”, Sb. Math., 205:10 (2014), 1413–1441  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. S. I. Kalmykov, “On some rational functions which are analogues of Chebyshev polynomials”, J. Math. Sci. (N. Y.), 207:6 (2015), 874–884  mathnet  crossref
    15. S.I. Kalmykov, B. Nagy, “Polynomial and rational inequalities on analytic Jordan arcs and domains”, Journal of Mathematical Analysis and Applications, 2015  crossref  mathscinet  scopus
    16. Totik V., “Bernstein- and Markov-Type Inequalities For Trigonometric Polynomials on General Sets”, Int. Math. Res. Notices, 2015, no. 11, 2986–3020  crossref  mathscinet  zmath  isi  elib  scopus
    17. Kalmykov S., Nagy B., Totik V., “Bernstein- and Markov-Type Inequalities For Rational Functions”, Acta Math., 219:1 (2017), 21–63  crossref  mathscinet  zmath  isi  scopus
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