Spaces Of Measures And Their Applications To Structured Population Models

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Spaces of Measures and their Applications to Structured Population Models

Author: Christian Düll
language: en
Publisher: Cambridge University Press
Release Date: 2021-10-07
Presents a comprehensive analytical framework for structured population models in spaces of Radon measures and their numerical approximation.
Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators

Author: Horst R. Thieme
language: en
Publisher: American Mathematical Society
Release Date: 2024-05-07
A fundamental question in the theory of discrete and continuous-time population models concerns the conditions for the extinction or persistence of populations – a question that is addressed mathematically by persistence theory. For some time, it has been recognized that if the dynamics of a structured population are mathematically captured by continuous or discrete semiflows and if these semiflows have first-order approximations, the spectral radii of certain bounded linear positive operators (better known as basic reproduction numbers) act as thresholds between population extinction and persistence. This book combines the theory of discrete-time dynamical systems with applications to population dynamics with an emphasis on spatial structure. The inclusion of two sexes that must mate to produce offspring leads to the study of operators that are (positively) homogeneous (of degree one) and order-preserving rather than linear and positive. While this book offers an introduction to ordered normed vector spaces, some background in real and functional analysis (including some measure theory for a few chapters) will be helpful. The appendix and selected exercises provide a primer about basic concepts and about relevant topics one may not find in every analysis textbook.
Geometry of the Phase Retrieval Problem

Author: Alexander H. Barnett
language: en
Publisher: Cambridge University Press
Release Date: 2022-05-05
This book provides a theoretical foundation and conceptual framework for the problem of recovering the phase of the Fourier transform.