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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
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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.


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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