Description

Book Synopsis
This is the first textbook-type presentation of tropical value distribution theory. It provides a detailed introduction of the tropical version of the Nevanlinna theory, describing growth and value distribution analysis of continuous, piecewise linear functions on the real axis. The book also includes applications of this theory to ultra-discrete equations. Three appendices are given to compare the contents of the theory with the classical counterparts in complex analysis.Detailed presentation of the proofs makes the book accessible for lecture courses and independent studies at the graduate and post-doctoral level.

Table of Contents
Tropical Polynomials, Rationals and Exponentials; Tropical Entire Functions; One-dimensional Tropical Nevanlinna Theory; Clunie and Mohon'ko Type Theorems; Tropical Holomorphic Curves; Representations of Tropical Periodic Functions; Applications to Ultra-Discrete Equations; Appendices: Classical Nevanlinna and Cartan Theories; Introduction to Ultra-Discrete Painleve Equations; Some Operators in Complex Analysis;

Tropical Value Distribution Theory And

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    A Hardback by Risto Korhonen, Ilpo Laine, Kazuya Tohge

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      Book details

      Publisher World Scientific Publishing Co Pte Ltd
      Published 18 May 2015
      ISBN-13 9789814632799
      978-9814632799
      ISBN-10 9814632791

      Description

      Book Synopsis
      This is the first textbook-type presentation of tropical value distribution theory. It provides a detailed introduction of the tropical version of the Nevanlinna theory, describing growth and value distribution analysis of continuous, piecewise linear functions on the real axis. The book also includes applications of this theory to ultra-discrete equations. Three appendices are given to compare the contents of the theory with the classical counterparts in complex analysis.Detailed presentation of the proofs makes the book accessible for lecture courses and independent studies at the graduate and post-doctoral level.

      Table of Contents
      Tropical Polynomials, Rationals and Exponentials; Tropical Entire Functions; One-dimensional Tropical Nevanlinna Theory; Clunie and Mohon'ko Type Theorems; Tropical Holomorphic Curves; Representations of Tropical Periodic Functions; Applications to Ultra-Discrete Equations; Appendices: Classical Nevanlinna and Cartan Theories; Introduction to Ultra-Discrete Painleve Equations; Some Operators in Complex Analysis;

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