Localization and Perturbation of Zeros of Entire Functions (Lecture Notes in Pure and Applied Mathematics)
Language: English
Published by Chapman and Hall/CRC, 2009
Series: Book 41 of 142 - Lecture Notes in Pure and Applied Mathematics
- Hardcover
- Used
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- Title
- Localization and Perturbation of Zeros of Entire Functions (Lecture Notes in Pure and Applied Mathematics)
- Author
- Gil*, Michael
- Publisher
- Chapman and Hall/CRC
- Publication year
- 2009
- Condition
- Like New
- Book Type
- book
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 1439800324
- ISBN 13
- 9781439800324
- Series
- Book 41 of 142: Lecture Notes in Pure and Applied Mathematics
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.
"Synopsis" may belong to another edition of this title.
About the Author
Michael Gil’ is a professor in the Department of Mathematics at Ben Gurion University of the Negev in Israel.
"About the title" may belong to another edition of this title.
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