Localization and Perturbation of Zeros of Entire Functions (Lecture Notes in Pure and Applied Mathematics, 258, Band 258) - Hardcover

Gil, Michael

Hardcover

ISBN 10: 1439800324 ISBN 13: 9781439800324

Verlag: Chapman and Hall/CRC, 2009

Inhaltsangabe

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.

Über diesen Titel

Über die Autorin bzw. den Autor

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

Von der hinteren Coverseite

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.

Details zur Ausgabe

• Verlag: Chapman and Hall/CRC
• Erscheinungsdatum: 2009
• Sprache: Englisch
• ISBN 10: 1439800324
• ISBN 13: 9781439800324
• Einband: Gebundene Ausgabe
• Auflage: 1
• Anzahl der Seiten: 300
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: gpsr@libri.de; gpsr@libri.de; ; Europaallee 1; Bad Hersfeld; 36244; Deutschland