Asymptotic characteristics of entire functions and their applications in mathematics and biophysics

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Asymptotic characteristics of entire functions and their applications in mathematics and biophysics / by L.S. Maergoiz

版:: 2nd ed., rev. and enl
資料種別:: 図書
出版情報:: Dordrecht ; Boston ; London : Kluwer Academic, c2003
形態:: xxiv, 362 p. ; 25 cm
シリーズ名:: Mathematics and its applications ; v. 559 <BA00044495>
著者名:: Maergoĭz, L. S. <DA14161041>
ISBN:: 9781402014628 [1402014627]
書誌ID:: BA63694848

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その他の標題:

Asimptoticheskie kharakteristiki t︠s︡elykh funkt︠s︡iĭ i ikh prilozhenii︠a︡ v matematike i biofizike

注記:

Bibliography: p. 348-360

主題:

Functions, Entire

言語:

英語

目次情報:

From the Editors of Russian Edition

Foreword to the Russian Edition

Introduction

Preliminary / Chapter 1：

On the growth of nondecreasing functions of one variable / 1.1：

Semicontinuous functions / 1.2：

Convex sets and associated functions / 1.3：

Convex functions / 1.4：

Duality of convex functions / 1.5：

Asymptotic properties of convex functions / 1.6：

Minkowski theorem on convex bodies / 1.7：

Plurisubharmonic functions / 1.8：

Trigonometrically [rho]-convex functions / 1.9：

Selected facts about entire functions of one variable / 1.10：

A Method of Identifying Homeostasis Relaxation Characteristics / Chapter 2：

Homeostasis system relaxation characteristics and the problem of their identification / 2.1：

Algorithm of recovering a quasipolinomial by its moments / 2.2：

Algorithm of approximation of discrete functions by quasipolinomials (identification algorithm) / 2.3：

The case of quasipolynomials of order 2 and 3 / 2.4：

The case of wave-type homeostasis processes / 2.5：

Indicator Diagram of an Entire Function of One Variable with Nonnegative Indicator / Chapter 3：

Plane [rho]-convex sets and the indicator diagram / 3.1：

Analog of the Polya theorem for an entire function of order [rho] [not equal] 1 and with nonnegative indicator / 3.2：

The generalized Borel polygon of a power series / 3.3：

Plane Indicator Diagram of Entire Function of Order [rho] [greater than sign] 0 with the Indicator of General Form / Chapter 4：

Minimal trigonometrically [rho]-convex functions / 4.1：

Many-sheeted diagrams associated with the functions of class P[subscript rho] / 4.2：

The relationship of the polynomials [alpha](z) = z[superscript rho] + a[subscript 1]z[superscript rho-1] + ... + a[subscript n]z[superscript rho-n] with functions of class M[subscript rho] / 4.3：

Plane ([rho],[alpha])-convex sets and the plane indicator diagram of an entire function of order [rho] [greater than sign] 0 / 4.4：

Spaces of Entire Functions of Order [rho] [greater than sign] 0 with Restrictions on the indicator / Chapter 5：

Entire function of two variables associated with a polynomial in [Beta subscript rho](l) / 5.1：

The analog of Borel's transformation and realization of the spaces [rho], h([theta])), [rho], h([theta])] / 5.2：

Applications of the analog of the Polya theorem / 5.3：

Geometrical Analysis of Asymptotics of Functions Plurisubgarmonic in C[superscript n] / Chapter 6：

Simplest properties of functions of classes [Beta], U / 6.1：

Various definitions of orders of functions of class U / 6.2：

Local A[subscript Phi]-type structure for function [Phi] in U / 6.3：

Global A[subscript Phi]-type structure for function [Phi] in U / 6.4：

Growth Characteristics of Entire Functions (Orders, Types) and Their Applications / Chapter 7：

Relationship between the growth characteristics of an entire function and its Taylor coefficients / 7.1：

Existence of entire functions with prescribed growth characteristics / 7.2：

The modulus maximum and the maximal term of an entire function: comparative growth / 7.3：

On the growth of the Nevanlinna characteristic for an entire function of several variables / 7.4：

Indicator Diagram of an Entire Function of Several Variables with Nonnegative Indicator / Chapter 8：

System of indicators and indicator diagrams of an entire function of several variables / 8.1：

Circular sets and their properties / 8.2：

An analog of the Polya-Martineau-Ehrenpreis Theorem / 8.3：

Consequences from Theorem 8.3.1 / 8.4：

Riemann Surface of the Inverse Function for a Polynomial of Fractional Order / Appendix A：

Some topological information / A.1：

Construction of the Riemann surface in question and its properties / A.2：

Indicator and Conjugate Diagrams of Entire Function of a Given Proximate Order / Appendix B：

Necessary information about proximate orders. Indicator diagram / B.1：

Analytic proximate orders and associated functions / B.2：

Entire functions associated with an analytic proximate order / B.3：

Entire function of a given proximate order and with nonnegative indicator / B.4：

Analytic proximate orders generated by entire or meromorphic functions / B.5：

Applications of the preceding results / B.6：

Comments

Bibliography

References to Chapters 1, 3-8

References to Chapter 2

Notation

From the Editors of Russian Edition

Foreword to the Russian Edition

Introduction

Preliminary / Chapter 1：

On the growth of nondecreasing functions of one variable / 1.1：

Semicontinuous functions / 1.2：

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