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Mat. Sb. (N.S.), 1969, Volume 79(121), Number 4(8), Pages 463–476 (Mi msb3599)  

This article is cited in 29 scientific papers (total in 29 papers)

On rays of completely regular growth of an entire function

V. S. Azarin


Abstract: This paper solves the problem of approximating a function, subharmonic in the entire plane, in a neighborhood of infinity by the logarithm of the modulus of an entire function. As an application of this result, we prove the existence of entire functions with an arbitrary closed set of rays of completely regular growth.
Bibliography: 8 titles.

Full text: PDF file (1100 kB)
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English version:
Mathematics of the USSR-Sbornik, 1969, 8:4, 437–450

Bibliographic databases:

UDC: 517.535.4
MSC: 30D15, 30D10, 31A05
Received: 15.11.1968

Citation: V. S. Azarin, “On rays of completely regular growth of an entire function”, Mat. Sb. (N.S.), 79(121):4(8) (1969), 463–476; Math. USSR-Sb., 8:4 (1969), 437–450

Citation in format AMSBIB
\Bibitem{Aza69}
\by V.~S.~Azarin
\paper On rays of completely regular growth of an~entire function
\jour Mat. Sb. (N.S.)
\yr 1969
\vol 79(121)
\issue 4(8)
\pages 463--476
\mathnet{http://mi.mathnet.ru/msb3599}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=257357}
\zmath{https://zbmath.org/?q=an:0194.10701|0197.35502}
\transl
\jour Math. USSR-Sb.
\yr 1969
\vol 8
\issue 4
\pages 437--450
\crossref{https://doi.org/10.1070/SM1969v008n04ABEH001123}


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

    This publication is cited in the following articles:
    1. V. S. Azarin, “Example of an entire function with given indicator and lower indicator”, Math. USSR-Sb., 18:4 (1972), 541–558  mathnet  crossref  mathscinet  zmath
    2. V. S. Azarin, “On the decomposition of an entire function of finite order into factors having given growth”, Math. USSR-Sb., 19:2 (1973), 225–226  mathnet  crossref  mathscinet  zmath
    3. V. S. Azarin, “On the asymptotic behavior of subharmonic functions of finite order”, Math. USSR-Sb., 36:2 (1980), 135–154  mathnet  crossref  mathscinet  zmath  isi
    4. R. S. Yulmukhametov, “Approximation of subharmonic functions”, Math. USSR-Sb., 52:2 (1985), 387–406  mathnet  crossref  mathscinet  zmath
    5. B. N. Khabibullin, “Comparison of subharmonic functions by means of their associated measures”, Math. USSR-Sb., 53:2 (1986), 523–539  mathnet  crossref  mathscinet  zmath
    6. O. V. Epifanov, “A homogeneous equation of convolution type in a space of analytic functions”, Math. USSR-Izv., 27:1 (1986), 85–100  mathnet  crossref  mathscinet  zmath
    7. B. N. Khabibullin, “Balayage on a system of rays and entire functions of completely regular growth”, Math. USSR-Izv., 38:1 (1992), 179–197  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. A. S. Krivosheev, V. V. Napalkov, “Complex analysis and convolution operators”, Russian Math. Surveys, 47:6 (1992), 1–56  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. A. B. Sekerin, “A local integral representation of strictly plurisubharmonic functions”, Math. Notes, 53:6 (1993), 635–639  mathnet  crossref  mathscinet  zmath  isi  elib
    10. R. S. Yulmukhametov, “Entire functions of several variables with given behaviour at infinity”, Izv. Math., 60:4 (1996), 857–876  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. J. Bonet, S.N. Melikhov, “Interpolation of Entire Functions and Projective Descriptions”, Journal of Mathematical Analysis and Applications, 205:2 (1997), 454  crossref  mathscinet  zmath
    12. R. S. Yulmukhametov, “Entire Functions with Given Asymptotic Behavior”, Funct. Anal. Appl., 32:3 (1998), 183–191  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. R. S. Yulmukhametov, “Solution of the Ehrenpreis factorization problem”, Sb. Math., 190:4 (1999), 597–629  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. Yuril Lyubarskii, Eugenia Malinnikova, “On approximation of subharmonic functions”, J Anal Math, 83:1 (2001), 121  crossref  mathscinet  isi  elib
    15. B. N. Khabibullin, “An approximation theorem for entire functions of exponential type and stability of zero sequences”, Sb. Math., 195:1 (2004), 135–148  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. I. Chizhikov, “Approximation of subharmonic functions”, St. Petersburg Math. J., 16:3 (2005), 591–607  mathnet  crossref  mathscinet  zmath
    17. M. A. Hirnyk, “Approximation of Subharmonic Functions in the Half-Plane by the Logarithm of the Modulus of an Analytic Function”, Math. Notes, 78:4 (2005), 447–455  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    18. M. A. Hirnyk, “Exactness of approximation of a subharmonic function by the logarithm of the modulus of an analytic function in the Chebyshev metric”, J. Math. Sci. (N. Y.), 139:2 (2006), 6393–6402  mathnet  crossref  mathscinet  zmath  elib
    19. A. V. Abanin, “Ob odnom primenenii slabo dostatochnykh mnozhestv”, Vladikavk. matem. zhurn., 7:2 (2005), 11–16  mathnet  mathscinet  elib
    20. Igor Chyzhykov, Oleh Skaskiv, “On an Asymptotic Equality Between the Minimum and the Maximum of δ-Subharmonic Functions of Zero Genus”, Comput. Methods Funct. Theory, 4:2 (2005), 447  crossref  mathscinet  zmath
    21. E. G. Kudasheva, B. N. Khabibullin, “Variation of subharmonic function under transformation of its Riesz measure”, Zhurn. matem. fiz., anal., geom., 3:1 (2007), 61–94  mathnet  mathscinet  zmath  elib
    22. V. I. Lutsenko, R. S. Yulmukhametov, “O tochnosti asimptoticheskoi approksimatsii subgarmonicheskikh funktsii logarifmom modulya tseloi funktsii”, Ufimsk. matem. zhurn., 2:3 (2010), 46–53  mathnet  zmath  elib
    23. R. A. Bashmakov, A. A. Putintseva, R. C. Yulmukhametov, “Entire functions of sine type and their applications”, St. Petersburg Math. J., 22:5 (2011), 737–750  mathnet  crossref  mathscinet  zmath  isi
    24. K. P. Isaev, R. S. Yulmukhametov, A. A. Yunusov, “Entire functions with fine asymptotic estimates for convex functions”, Ufa Math. J., 6:2 (2014), 35–43  mathnet  crossref  elib
    25. K. P. Isaev, K. V. Trounov, R. S. Yulmukhametov, “Representation of functions in locally convex subspaces of $A^\infty (D)$ by series of exponentials”, Ufa Math. J., 9:3 (2017), 48–60  mathnet  crossref  isi  elib
    26. G. G. Braichev, V. B. Sherstyukov, “Tochnye otsenki asimptoticheskikh kharakteristik rosta tselykh funktsii s nulyami na zadannykh mnozhestvakh”, Fundament. i prikl. matem., 22:1 (2018), 51–97  mathnet
    27. K. P. Isaev, “Predstavlyayuschie sistemy eksponent v prostranstvakh analiticheskikh funktsii”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 3–64  mathnet  mathscinet
    28. V. B. Sherstyukov, “Asimptoticheskie svoistva tselykh funktsii s zadannym zakonom raspredeleniya kornei”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 104–129  mathnet  mathscinet
    29. B. N. Khabibullin, A. V. Shmeleva, Z. F. Abdullina, “Vymetanie mer i subgarmonicheskikh funktsii na sistemu luchei. II. Vymetaniya konechnogo roda i regulyarnost rosta na odnom luche”, Algebra i analiz, 32:1 (2020), 208–243  mathnet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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