Baernstein's thesis and entire functions with negative zeros

D.Drasin

1. A. Baernstein II, A nonlinear tauberian theorem in function theory, Amer. Math. Soc. Transactions 146 (1969), 87--105.

2. A. Baernstein II, How the $*$-function solves extremal problems, in Proceedings of the International Congress of Mathematicians (Helsinki, 1978) Acad. Sci. Fennica, Helsinki (1980) 639--644.

3. D. Drasin, Two examples, Institut Mittag-Leffler technical report -- 8 (1977).

4. D. Drasin, Approximation of subharmonic functions with applications, in Approximation, complex analysis, and potential theory (Montreal, QC, 2000), 163--189, NATO Sci. Ser. II Math. Phys. Chem., 37, Kluwer Acad. Publ., Dordrecht, 2001.

5. D. Drasin, A. Weitsman, Meromorphic functions with large sums of deficiencies, Advances in Math. 15 (1975), 93--126.

6. A. Edrei, Sums of deficiencies of meromorphic functions, J. Anal. Math. 14 (1965), 79--107.

7. A. Edrei, Solution of the deficiency problem for functions of small lower order, Proc. London Math. Soc. 26 (1973), №3, 435--445.

8. A. Edrei, W.H.J. Fuchs, Tauberian theorems for a class of meromorphic functions with negative zeros and positive poles, in Contemporary problems in theory anal. functions (Internat. Conf., Erevan, 1965), ``Nauka'', Moscow, 1966, 339--358. (Russian)

9. A.A. Gol'dberg, O.N. Fridman, Regular growth of meromorphic functions with positive zeros and negative poles, Vesnik Lviv. Derzh. Univ. Ser. Mekh.-Mat. 14 (1979), 13--18. (Ukrainian, Russian summary)

10. A.A. Gol'dberg, I.V. Ostrovskii, Distribution of values of meromorphic functions, Izdat. ``Nauka'', Moscow, 1970. (Russian)

11. W.K. Hayman, Meromorphic Functions, Oxford, 1964.

12. W.K. Hayman, P.B. Kennedy, Subharmonic functions, V.1, Academic Press, 1976.

13. S. Hellerstein, J. Williamson, Entire functions with negative zeros and a problem of R. Nevanlinna, J.~Anal. Math. 22 (1969), 233--267.

14. S. Hellerstein, D.F. Shea, J. Williamson, A tauberian theorem characterizing the regularity of growth of a class of entire functions, Duke Math. J. 37 (1970) 489--499.

15. G.R. MacLane, A growth condition for class $\mathcal{A}$, Michigan Math. J. 25 (1978), 263--287.

16. R.S. Yulmukhametov, Approximation of subharmonic functions, Anal. Math. 11 (1985), 257--282. (Russian)

	Baernstein's thesis and entire functions with negative zeros
Author	D.Drasin drasin@math.purdue.edu Department of Mathematics, Purdue University, West Lafayette, IN 47906
Abstract	We give a new proof of Baernstein's theorem on asymptotic of zeros of an entire function of regular growth.
Keywords	entire function, negative zero, Baernstein theorem, regular growth
DOI	doi:10.30970/ms.34.2.160-167
Reference	1. A. Baernstein II, A nonlinear tauberian theorem in function theory, Amer. Math. Soc. Transactions 146 (1969), 87--105. 2. A. Baernstein II, How the $*$-function solves extremal problems, in Proceedings of the International Congress of Mathematicians (Helsinki, 1978) Acad. Sci. Fennica, Helsinki (1980) 639--644. 3. D. Drasin, Two examples, Institut Mittag-Leffler technical report -- 8 (1977). 4. D. Drasin, Approximation of subharmonic functions with applications, in Approximation, complex analysis, and potential theory (Montreal, QC, 2000), 163--189, NATO Sci. Ser. II Math. Phys. Chem., 37, Kluwer Acad. Publ., Dordrecht, 2001. 5. D. Drasin, A. Weitsman, Meromorphic functions with large sums of deficiencies, Advances in Math. 15 (1975), 93--126. 6. A. Edrei, Sums of deficiencies of meromorphic functions, J. Anal. Math. 14 (1965), 79--107. 7. A. Edrei, Solution of the deficiency problem for functions of small lower order, Proc. London Math. Soc. 26 (1973), №3, 435--445. 8. A. Edrei, W.H.J. Fuchs, Tauberian theorems for a class of meromorphic functions with negative zeros and positive poles, in Contemporary problems in theory anal. functions (Internat. Conf., Erevan, 1965), ``Nauka'', Moscow, 1966, 339--358. (Russian) 9. A.A. Gol'dberg, O.N. Fridman, Regular growth of meromorphic functions with positive zeros and negative poles, Vesnik Lviv. Derzh. Univ. Ser. Mekh.-Mat. 14 (1979), 13--18. (Ukrainian, Russian summary) 10. A.A. Gol'dberg, I.V. Ostrovskii, Distribution of values of meromorphic functions, Izdat. ``Nauka'', Moscow, 1970. (Russian) 11. W.K. Hayman, Meromorphic Functions, Oxford, 1964. 12. W.K. Hayman, P.B. Kennedy, Subharmonic functions, V.1, Academic Press, 1976. 13. S. Hellerstein, J. Williamson, Entire functions with negative zeros and a problem of R. Nevanlinna, J.~Anal. Math. 22 (1969), 233--267. 14. S. Hellerstein, D.F. Shea, J. Williamson, A tauberian theorem characterizing the regularity of growth of a class of entire functions, Duke Math. J. 37 (1970) 489--499. 15. G.R. MacLane, A growth condition for class $\mathcal{A}$, Michigan Math. J. 25 (1978), 263--287. 16. R.S. Yulmukhametov, Approximation of subharmonic functions, Anal. Math. 11 (1985), 257--282. (Russian)
Pages	160-167
Volume	34
Issue	2
Year	2010
Journal	Matematychni Studii
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