References
V. S. Azarin,On rays of completely regular growth of an entire function, Math. USSR Sb.8 (1969), 437–450.
A. Beurling inThe Collected Works of Arne Beurling (L. Carleson, P. Malliavin, J. Neuberger and J. Wermer, eds.), Birkhäuser, Boston, 1989, pp. 341–365.
A. Beurling and P. Malliavin,On Fourier transforms of measures with compact support, Acta Math.107 (1962), 291–309.
M. Christ, On the\(\bar \partial \) equation in weighted L2 norms in\(\bar \partial \), J. Geom. Anal.1 (1991), 193–230.
D. Drasin,Approximation of subharmonic functions with applications, preprint, Montréal, 2000.
A. Goldberg and M. Himyk,Approximation of subharmonic functions by logarithms of moduli of entire functions in integral metrics, preprint, 1999.
A. F. Grishin, Private communication, 1975.
W. K. Hayman,Subharmonic Functions, Vol. 2, Academic Press, London, New York, 1989.
W. Al-Katifi,On the asymptotic values and paths of certain integral and meromorphic functions, Proc. London. Math. Soc.16 (1966), 599–634.
P. B. Kennedy,A class of integral functions bounded on certain curves, Proc. London. Math. Soc.6 (1956), 518–547.
B. Kjellberg,On Certain Integral and Harmonic Functions. A Study in Minimum Modulus, Thesis, University of Uppsala, 1948.
J. Korevaar and M. A. Monterie,Approximation of the equilibrium distribution by distributions of equal point charges with minimal energy, Trans. Amer. Math. Soc.350 (1998), 2329–2348.
B. Ja. Levin,Distribution of Zeros of Entire Functions, Amer. Math. Soc., Providence, RI, 1980.
Yu. Lyubarskii and K. Seip,Sampling and interpolation of entire functions and exponential systems in convex domains, Ark. Mat.32 (1994), 157–193.
Yu. I. Lyubarskii and M. L. Sodin,Analogues of Sine Type Function for Convex Domains, Preprint no. 17, Institute for Low Temperatures, Ukrainian Acad. Sci., Kharkov, 1986 (Russian).
S. N. Mergeljan,On the completeness of systems of analytic functions, Amer. Math. Soc. Transl. Ser. 219 (1962), 109–166.
F. Nazarov, S. Treil and A. Volberg,Cauchy integral and Calderón-Zygmund operators on nonhomogeneous spaces, Internat. Math. Res. Notices no. 15 (1997), 703–726.
J. Ortega-Cerdà, Multipliers and weighted\(\bar \partial \) estimates, preprint, 1999.
J. Ortega-Cerdà and K. Seip,Beurling-type density theorems for weighted L p spaces of entire functions, J. Analyse Math.75 (1998), 247–266.
Ortega-Cerdà and K. Seip,Multipliers for entire functions and an interpolation problem of Beurling, J. Funct. Anal.162 (1999), 400–415.
E. M. Stein,Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970.
R. S. Yulmukhametov,Approximation of subharmonic functions, Anal. Math.11 (1985), no. 3, 257–282 (Russian).
Author information
Authors and Affiliations
Corresponding author
Additional information
Partly supported by NATO Science Fellowship and Norwegian Research Council project 132386/410.
Rights and permissions
About this article
Cite this article
Lyubarskii, Y., Malinnikova, E. On approximation of subharmonic functions. J. Anal. Math. 83, 121–149 (2001). https://doi.org/10.1007/BF02790259
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02790259