Riesz measure of functions that are subharmonic in the exterior of a compact(in Russian)

Author
S. Ju. Favorov, L. D. Radchenko
V.N. Karazin Kharkiv National University
Abstract
We consider subharmonic functions in the exterior of a compact set in a finite-dimensional space that grows near the compact. We assume that the compact has some generalized convex property. We get an integral condition on function's Riesz measure and check its accuracy.
Keywords
Blaschke condition; subharmonic function; analytic function; Riesz measure
Reference
1. S. Favorov, L. Golinskii, A Blaschke-type condition for analytic and subharmonic functions and application to contraction operators, Amer. Math. Soc. Transl. (2), 226 (2009), 37–47.

2. S. Favorov, L. Golinskii, Blaschke-type conditions on unbounded domains, generalized convexity and applications in perturbation theory, to appear.

3. S.Yu. Favorov, L.B. Golinskii. Blaschke-Type Conditions for Analytic and Subharmonic Functions in the Unit Disk, Local Analogs and Inverse Problems, Computational Methods and Function Theory, 12 (2012), ¹1, 151–166.

4. L.D. Radchenko, S.Yu. Favorov, An analytical andsubharmonic functions in a disk near the growing part of the boundary, in printing. (in Russian)

5. G. Kramer, Mathematical Methods of Statistics, M., Mir, 1975, 648 p. (in Russian)

6. J. Garnett, Bounded analytic functions, Graduate Texts in Mathematics, V.236, Springer, New York, 2007.

7. A. Borichev, L. Golinskii, S. Kupin, A Blaschke-type condition and its application to complex Jacobi matrices, Bull. London Math. Soc., 41 (2009), 117–123.

8. W.K. Hayman, P.B. Kennedy, Subharmonic functions, Academic Press Inc., London, LTD, 1976, 304 p.

9. M.M. Djrbashian, Theory of Factorization of Functions Meromorphic in the Disk, In: Proceedings of the ICM, Vancouver, B.C., 2 (1974), 197–202.

10. W.K. Hayman, B. Korenblum, A critical growth rate for functions regular in a disk, Michigan Math. J., 27 (1980), 21–30.

11. F.A. Shamoyan, On zeros of analytic in the disc functions growing near its boundary, Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 18 (1983), ¹1.

12. A.M. Jerbashian, On the theory of weighted classes of area integrable regular functions, Complex Variables, 50 (2005), 155–183.

13. P.H. Armitage, S.J. Gardnier, Classical potential theory, Springer, 2002, 333 p.

14. E. Lieb, M. Loss, Analysis, Graduate Studies in Mathematics, V.14, AMS, Providence, RI, 1997.

15. T. Ransford, Potential theory in the complex plane, London Math. Soc. Student Texts, V.28, Cambridge University Press, 1995.
Pages
149-158
Volume
40
Issue
2
Year
2013
Journal
Matematychni Studii
Full text of paper
pdf
Table of content of issue