An operator semigroup in mathematical genetics
type: Item
instance of: scholarly article
title: An operator semigroup in mathematical genetics
zbMATH Open document ID: 1335.92002
DOI: 10.1007/978-3-642-35958-3
author: Adam Bobrowski
author: Marek Kimmel
published in: SpringerBriefs in Applied Sciences and Technology
publication date: 2013-06-18T00:00:00Z
review text: The authors first describe some models for population dynamics such as the Cannings model and the Wright-Fisher model. Then, they introduce the Moran model for population genetics, which provides a way to define the master equation. Chapter 4 is devoted to describe mathematical tools for solving and investigating the asymptotic behavior of mild solutions to the master equation via semigroup theory. Here, there are facts about Banach spaces, bounded linear operators, semigroups of linear operators and their generators, the Markov semigroup and the concept of core of generators. Deriving the semigroup related to the master equation and its asymptotic behavior is the topic of the last chapter. This book is a very interesting readable descriptive text in one of the important branches of applied mathematics. It helps readers to gain insight about the application of such deep mathematical tools as the semigroup theory of linear operators in other branches of science.
reviewed by: Ruhollah Jahanipur
Mathematics Subject Classification ID: 92-02
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 47D07
zbMATH DE Number: 6176759
zbMATH Keywords: mathematical genetics
zbMATH Keywords: Wright-Fisher model
zbMATH Keywords: population dynamics
zbMATH Keywords: semigroup of operators
zbMATH Keywords: Markov semigroup
zbMATH Keywords: Kolmogorov matrices
Wikidata QID: Q59341324
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-642-35958-3
OpenAlex ID: W655910134
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description: scientific article; zbMATH DE number 6176759