Localization and Perturbation of Zeros of Entire Functions
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As the first book that presents a systematic exposition of bounds for the zeros of entire functions, this text offers a new approach to the investigation of entire functions based on estimates for the resolvents of compact operators. It focuses on bounds for the zeros and variations of zeros under perturbations while dealing with the operator approach to the theory of analytic functions. The book covers the well-known results of the Hadamard theorem, the Jensen inequality, the Ostrowski inequalities, and the Hurwitz theorem. It also investigates approximations of the sums of the Taylor series and the distance between zeroes of the Taylor series.
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.
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