Description
Localization and Perturbation of Zeros of Entire Functions
Lecture Notes in Pure and Applied Mathematics Series
Author: Gil' Michael
Language: EnglishSubject for Localization and Perturbation of Zeros of Entire Functions:
Keywords
Entire Functions; Unique Positive Root; Finite Matrices; Riemann Zeta Function; Eigenvalues of Compact Operators; Nilpotent Part; Polynomials; Hurwitz Theorem; Bounds for Zeros of Entire Functions; Total Multiplicity; Entire Matrix-Valued Functions; Canonical Product; Parseval Equality; Exponential Type; Taylor Coefficients; Nilpotent Operator; Hilbert Schmidt Norm; Dw; Weyl Inequalities; Positive Half Line; Orthogonal Normal Basis; Finite Zeros; Matrix Pencil; Linear Operator; Maximal Chain; Characteristic Values; Convergence Exponent; Open Left Half Plane; Multiplicative Representation; Previous Lemma
Publication date: 06-2017
· 15.6x23.4 cm · Paperback
Publication date: 12-2009
312 p. · 15.6x23.4 cm · Hardback
Description
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One of the most important problems in the theory of entire functions is the distribution of the zeros of entire functions. Localization and Perturbation of Zeros of Entire Functions is the first book to provide a systematic exposition of the bounds for the zeros of entire functions and variations of zeros under perturbations. It also offers a new approach to the investigation of entire functions based on recent estimates for the resolvents of compact operators.
After presenting results about finite matrices and the spectral theory of compact operators in a Hilbert space, the book covers the basic concepts and classical theorems of the theory of entire functions. It discusses various inequalities for the zeros of polynomials, inequalities for the counting function of the zeros, and the variations of the zeros of finite-order entire functions under perturbations. The text then develops the perturbation results in the case of entire functions whose order is less than two, presents results on exponential-type entire functions, and obtains explicit bounds for the zeros of quasipolynomials. The author also offers additional results on the zeros of entire functions and explores polynomials with matrix coefficients, before concluding with entire matrix-valued functions.
This work is one of the first to systematically take the operator approach to the theory of analytic functions.
Finite Matrices. Eigenvalues of Compact Operators. Some Basic Results of the Theory of Analytic Functions. Polynomials. Bounds for Zeros of Entire Functions. Perturbations of Finite-Order Entire Functions. Functions of Order Less than Two. Exponential-Type Functions. Quasipolynomials. Transforms of Finite-Order Entire Functions and Canonical Products. Polynomials with Matrix Coefficients. Entire Matrix-Valued Functions. Bibliography. Index.
Michael Gil’ is a professor in the Department of Mathematics at Ben Gurion University of the Negev in Israel.
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