Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Zero distribution for pairs of holomorphic functions with applications to eigenvalue distribution


Author: A. A. Shkalikov
Journal: Trans. Amer. Math. Soc. 281 (1984), 49-63
MSC: Primary 30D20; Secondary 47A70
DOI: https://doi.org/10.1090/S0002-9947-1984-0719658-8
MathSciNet review: 719658
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ f$ and $ g$ be holomorphic in an angle $ \Lambda $. Theorem 1 shows that the zero-distributions of $ f$ and $ g$ are comparable if, near $ \partial \Lambda $, $ f$ and $ g$ grow similarly. This result is applied to analyse the asymptotic behavior of eigenvalues of certain perturbed normal operators.


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

  • [1] V. A. Avakjan, Asymptotic distribution of eigenvalues of linear bundle perturbed by analytic operator-valued functions, Functional Anal. Appl. 12 (1978), 66-67. (Russian) MR 0500243 (58:17918)
  • [2] M. Sh. Birman and M. Z. Solomyak, Collection, Itogi Nauki i Tekhniki, Mathematicheskii Analiz, no. 14, VINITI, Moscow, 1977, pp. 5-58.
  • [3] M. L. Cartwright, Integral functions, Cambridge Univ. Press, New York, 1956. MR 0077622 (17:1067c)
  • [4] A. Edrei and W. H. J. Fuchs, On the growth of meromorphic functions with several deficient values, Trans. Amer. Math. Soc. 93 (1959), 292-328. MR 0109887 (22:770)
  • [5] -, Bounds for the number of deficient values of certain classes of meromorphic functions, Proc. London Math. Soc. 12 (1962), 315-344. MR 0138765 (25:2208)
  • [6] I. C. Gohberg and M. G. Krein, Introduction to the theory of linear non-self-adjoint operators, Transl. Math. Monos., vol. 18 , Amer. Math. Soc., Providence, R.I., 1969. MR 0246142 (39:7447)
  • [7] W. K. Hayman, Meromorphic functions, Oxford Univ. Press, London and New York, 1964. MR 0164038 (29:1337)
  • [8] M. V. Keldysh, Eigenvalues and eigenfunctions of certain classes of non-self-adjoint operators, Dokl. Akad. Nauk. SSSR 77 (1951), 11-14.
  • [9] B. Ja. Levin, Distribution of zeros of entire functions, Transl. Math. Monos., vol. 5 , Amer. Math. Soc., Providence, R.I., 1964. MR 0156975 (28:217)
  • [10] E. C. Titchmarsh, The theory of functions, Oxford Univ. Press, London and New York, 1939.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30D20, 47A70

Retrieve articles in all journals with MSC: 30D20, 47A70


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0719658-8
Keywords: Zero distribution of holomorphic functions, estimates of Blaschke product, eigenvalue distribution of perturbed normal operators
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society