Localization and Perturbation of Zeros of Entire Functions

One of the most important problems in the theory of entire functions is the distribution of the zeros of entire functions. This is the first book to provide a systematic exposition of the bounds for the zeros of entire functions and variations of zeros under perturbations. The book also offers a new approach for investigating entire functions based on recent estimates for the resolvents of compact operators. Along with describing applications to differential, functional differential, and difference equations, the author estimates the distance between the zeros of an entire function and its critical points as well as the distance between the zeros of the Taylor series and its tail.

Autorentext

Michael Gil' is a professor in the Department of Mathematics at Ben Gurion University of the Negev in Israel.

Inhalt

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.