Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Approximation of subharmonic functions


Author: I. Chyzhykov
Translated by: the author
Original publication: Algebra i Analiz, tom 16 (2004), nomer 3.
Journal: St. Petersburg Math. J. 16 (2005), 591-607
MSC (2000): Primary 30A05; Secondary 30D20, 30E10
Published electronically: May 2, 2005
MathSciNet review: 2083571
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In certain classes of subharmonic functions $u$on $\mathbb C$ distinguished in terms of lower bounds for the Riesz measure of $u$, a sharp estimate is obtained for the rate of approximation by functions of the form $\log \vert f(z)\vert$, where $f$ is an entire function. The results complement and generalize those recently obtained by Lyubarskii and Malinnikova.


References [Enhancements On Off] (What's this?)

  • 1. W. K. Hayman and P. B. Kennedy, Subharmonic functions. Vol. I, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1976. London Mathematical Society Monographs, No. 9. MR 0460672
  • 2. V. S. Azarin, The rays of completely regular growth of an entire function, Mat. Sb. (N.S.) 79 (121) (1969), 463–476 (Russian). MR 0257357
  • 3. Yu. I. Lyubarskii and M. L. Sodin, Analogs of sinus type functions for convex domains, Preprint no. B17, Fiz.-Tekhn. Inst., Akad. Nauk USSR, Khar'kov, 1986. (Russian)
  • 4. David Drasin, Approximation of subharmonic functions with applications, Approximation, complex analysis, and potential theory (Montreal, QC, 2000), NATO Sci. Ser. II Math. Phys. Chem., vol. 37, Kluwer Acad. Publ., Dordrecht, 2001, pp. 163–189. MR 1873588, 10.1007/978-94-010-0979-9_6
  • 5. David Drasin, On Nevanlinna’s inverse problem, Complex Variables Theory Appl. 37 (1998), no. 1-4, 123–143. MR 1687865
  • 6. I. E. Chyzhykov, On minimum modulus of an entire function of zero order, Mat. Stud. 17 (2002), no. 1, 41–46 (English, with English and Russian summaries). MR 1932269
  • 7. R. S. Yulmukhametov, Approximation of subharmonic functions, Anal. Math. 11 (1985), no. 3, 257–282 (Russian, with English summary). MR 822590, 10.1007/BF01907421
  • 8. R. S. Yulmukhametov, Approximation of homogeneous subharmonic functions, Mat. Sb. (N.S.) 134(176) (1987), no. 4, 511–529, 576 (Russian); English transl., Math. USSR-Sb. 62 (1989), no. 2, 507–523. MR 933700
  • 9. Markiyan Girnyk and Anatolii Goldberg, Approximation of subharmonic functions by logarithms of moduli of entire functions in integral metrics, Entire functions in modern analysis (Tel-Aviv, 1997) Israel Math. Conf. Proc., vol. 15, Bar-Ilan Univ., Ramat Gan, 2001, pp. 117–135. MR 1890534
  • 10. Yurii Lyubarskii and Eugenia Malinnikova, On approximation of subharmonic functions, J. Anal. Math. 83 (2001), 121–149. MR 1828489, 10.1007/BF02790259
  • 11. V. P. Havin and N. K. Nikolski (eds.), Linear and complex analysis. Problem book 3. Part II, Lecture Notes in Mathematics, vol. 1574, Springer-Verlag, Berlin, 1994. MR 1334346
  • 12. Igor Chyzhykov, Approximation of subharmonic functions of slow growth, Mat. Fiz. Anal. Geom. 9 (2002), no. 3, 509–520. MR 1949807
  • 13. A. F. Grishin and S. V. Makarenko, On a theorem of Yulmukhametov, Mat. Zametki 67 (2000), no. 6, 859–862 (Russian, with Russian summary); English transl., Math. Notes 67 (2000), no. 5-6, 724–726. MR 1820640, 10.1007/BF02675626

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 30A05, 30D20, 30E10

Retrieve articles in all journals with MSC (2000): 30A05, 30D20, 30E10


Additional Information

I. Chyzhykov
Affiliation: Faculty of Mechanics and Mathematics, Ivan Franko National University, Lviv, Ukraine
Email: tftj@franko.lviv.ua chyzh@lviv.farlep.net

DOI: http://dx.doi.org/10.1090/S1061-0022-05-00867-8
Received by editor(s): May 12, 2003
Published electronically: May 2, 2005
Additional Notes: Partially supported by the scholarship of the Queen Jadwiga Foundation, Jagellonian University (Kraków, Poland)
Article copyright: © Copyright 2005 American Mathematical Society