Positive Operator Semigroups

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This book offers a gentle yet contemporary introduction to the theory of operator semigroups, essential for describing the dynamics of complex phenomena across various applications. It emphasizes the concept of positivity, a key characteristic in physical, chemical, biological, and economic processes, which enriches the mathematical structure of the associated dynamical systems and operators. The first part develops the finite dimensional theory in a coordinate-free manner, a rare approach in existing literature, effectively presenting the core ideas of the Perron-Frobenius theory applicable to infinite dimensions. It includes discussions on graph matrices, age-structured population models, and economic models. The second part delves into the infinite dimensional theory of positive operator semigroups, covering spectral and asymptotic theory, with recent applications such as population equations, neutron transport theory, delay equations, and flows in networks. Each chapter features numerous exercises, while an updated bibliography and detailed subject index support the reader's exploration. Targeted primarily at graduate and master students, the finite dimensional section is also accessible to advanced bachelor students with a solid foundation in linear algebra and calculus.