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.
- ISBN10 661290254X
- ISBN13 9786612902543
- Publish Date 4 December 2009
- Publish Status Active
- Out of Print 28 August 2012
- Publish Country US
- Publisher Taylor & Francis Ltd
- Imprint CRC Press
- Format eBook
- Pages 317
- Language English