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This monograph serves two primary purposes. First, it provides a comprehensive treatment of bi-continuous semigroup theory and its applications, ranging from network theory to control theory. The exposition proceeds systematically from fundamental theory through approximation methods, extrapolation techniques as well as perturbation theory, concluding with applications to networks, mean ergodicity and control systems. Each chapter includes illustrative examples to reinforce the theoretical concepts.
Second, this work aims at supporting emerging researchers and doctoral students by offering a structured foundation for further investigation in operator semigroups. By synthesizing current knowledge, it provides a reference point for new research projects in this domain.
Inhaltsverzeichnis
Introduction.- 1 An excursion on C0-semigroups.- 2 Bi-Continuous Semigroups: Preliminaries and Examples.- 3 The generator of bi-continuous semigroups.- 4 General Intermediate and Extrapolated Spaces.- 5 Intermediate and Extrapolation Spaces for Bi-Continuous Semigroups.- 6 Approximation of bi-continuous semigroups.- 7 Bounded and Miyadera-Voigt perturbations.- 8 Desch-Schappacher perturbations of bi-continuous semigroups.- 9 Bi-continuous Semigroups for Flows on Infinite Networks.- 10 Mean ergodic bi-continuous semigroups.- 11 Bi-continuous semigroups in control theory.- A The mixed topology.- B Riesz spaces and Banach lattices.- Bibliography.
Zusammenfassung
This monograph serves two primary purposes. First, it provides a comprehensive treatment of bi-continuous semigroup theory and its applications, ranging from network theory to control theory. The exposition proceeds systematically from fundamental theory through approximation methods, extrapolation techniques as well as perturbation theory, concluding with applications to networks, mean ergodicity and control systems. Each chapter includes illustrative examples to reinforce the theoretical concepts.
Second, this work aims at supporting emerging researchers and doctoral students by offering a structured foundation for further investigation in operator semigroups. By synthesizing current knowledge, it provides a reference point for new research projects in this domain.
