Lecture Notes in Pure and Applied Mathem Localization and Perturbation of Zeros of Entire Functions, (Paperback)

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.