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Synopsis
"Et moi9 .. ,' si j*avait su comment en revenir, je One service mathematics has rendered the n 'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded nonsense'. The series is divergent; therefore we may be Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought A highly necessary tool in a world where both feedback and nonlineari ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sci ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser vice topology has rendered mathematical physics .. .'; 'One service logic has rendered computer science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
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Synopsis
This monograph deals with functions of completely regular growth (FCRG), ie functions that have, in some sense, good asymptotic behaviour out of an exceptional set. The theory of entire functions of completely regular growth of one variable, developed in the late 1930s, soon found applications in both mathematics and physics. Later, the theory was extended to functions in the half-plane, subharmonic functions in space, and entire functions of several variables. This volume describes this theory and presents recent developments based on the concept of weak convergence. This enables a unified approach and provides a comparatively simple presentation of the classical Levin-Pfluger theory. Emphasis is put on those classes of functions which are particularly important for applications - functions having a bounded spectrum and finite exponential sums. While aimed at research mathematicians and physicists whose work involves complex analysis and its applications, the book should also be useful to those working in some areas of radiophysics and optics.
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Functions of Completely Regular Growth (Mathematics and its Applications, 81)
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Functions of Completely Regular Growth
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 1. Entire functions of completely regular growth of one variable.1. Preliminaries.2. Regularity of growth, D'-convergence and right distribution of zeros.3. Rays of completely regular growth. Addition of indicators.- Notes.- 2. Subharmonic functions of completely regular growth in Rn.1. General information on subharmonic functions. D\*-convergence .2. Criteria for regularity of growth in Rn.3. Rays of completely regular growth and limit sets.4. Addition of indicators.- Notes.- 3. Entire functions of completely regular growth in Cn.1. Functions of c completely regular growth on complex rays.2. Addition of indicators.3. Entire functions with prescribed behaviour at infinity.- Notes.- 4. Functions of completely regular growth in the half-plane or a cone.1. Preliminary information on functions holomorphic in a half-plane.2. Functions of completely regular growth in C+.3. Functions of completely regular growth in C+.4. Functions of completely regular growth in a cone.- Notes.- 5. Functions of exponential type and bounded on the real space (Fourier transforms of distribution of compact support).1. Regularity of growth of entire functions of exponential type and bounded on the real space.2. Discrete uniqueness sets.3. Norming sets.- Notes.- 6. Quasipolynomials.1. M-quasipolynomials. Growth and zero distribution.2. Entire functions that are quasipolynomials in every variable.3. Factors of quasipolynomials.- Notes.- 7. Mappings.1. Information on the general theory of holomorphic mappings.2. Plurisubharmonic functions of -regular growth and asymptotic behaviour of order functions of holomorphic mappings.3. Jessen's theorem for almost periodic holomorphic mappings.- Notes. Seller Inventory # 9780792316770
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Functions of Completely Regular Growth
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Functions of Completely Regular Growth
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Buch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -1. Entire functions of completely regular growth of one variable.- 1. Preliminaries.- 2. Regularity of growth, D'-convergence and right distribution of zeros.- 3. Rays of completely regular growth. Addition of indicators.- Notes.- 2. Subharmonic functions of completely regular growth in Rn.- 1. General information on subharmonic functions. D\*-convergence .- 2. Criteria for regularity of growth in Rn.- 3. Rays of completely regular growth and limit sets.- 4. Addition of indicators.- Notes.- 3. Entire functions of completely regular growth in Cn.- 1. Functions of c completely regular growth on complex rays.- 2. Addition of indicators.- 3. Entire functions with prescribed behaviour at infinity.- Notes.- 4. Functions of completely regular growth in the half-plane or a cone.- 1. Preliminary information on functions holomorphic in a half-plane.- 2. Functions of completely regular growth in C+.- 3. Functions of completely regular growth in C+.- 4. Functions of completely regular growth in a cone.- Notes.- 5. Functions of exponential type and bounded on the real space (Fourier transforms of distribution of compact support).- 1. Regularity of growth of entire functions of exponential type and bounded on the real space.- 2. Discrete uniqueness sets.- 3. Norming sets.- Notes.- 6. Quasipolynomials.- 1. M-quasipolynomials. Growth and zero distribution.- 2. Entire functions that are quasipolynomials in every variable.- 3. Factors of quasipolynomials.- Notes.- 7. Mappings.- 1. Information on the general theory of holomorphic mappings.- 2. Plurisubharmonic functions of -regular growth and asymptotic behaviour of order functions of holomorphic mappings.- 3. Jessen's theorem for almost periodic holomorphic mappings.- Notes.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 408 pp. Englisch. Seller Inventory # 9780792316770
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Functions of Completely Regular Growth
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -'Et moi9 . ,' si j avait su comment en revenir, je One service mathematics has rendered the n 'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded nonsense'. The series is divergent; therefore we may be Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought A highly necessary tool in a world where both feedback and nonlineari ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sci ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser vice topology has rendered mathematical physics . .'; 'One service logic has rendered computer science . .'; 'One service category theory has rendered mathematics . .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series. 408 pp. Englisch. Seller Inventory # 9780792316770
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Functions of Completely Regular Growth
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