One-Parameter Semigroups for Linear Evolution Equations

One-Parameter Semigroups for Linear Evolution Equations

2000 | Klaus-Jochen Engel, Rainer Nagel
The provided text is the preface and excerpt from the book "One-Parameter Semigroups for Linear Evolution Equations" by Klaus-Jochen Engel and Rainer Nagel. The book is part of the Graduate Texts in Mathematics series and is edited by S. Axler, F.W. Gehring, and K.A. Ribet. It covers the theory of one-parameter semigroups of linear operators on Banach spaces, starting with the Hille–Yosida generation theorem and progressing to advanced topics such as spectral theory, perturbation theory, and applications to various evolution equations. The authors emphasize the importance of strongly continuous semigroups and provide a comprehensive treatment of related concepts, including interpolation and extrapolation spaces, perturbation theorems, and approximation formulas. The book also includes historical perspectives and philosophical discussions on the relationship between semigroups and evolution equations, as well as determinism. The preface highlights the book's structure, intended audience, and contributions from various experts in the field.The provided text is the preface and excerpt from the book "One-Parameter Semigroups for Linear Evolution Equations" by Klaus-Jochen Engel and Rainer Nagel. The book is part of the Graduate Texts in Mathematics series and is edited by S. Axler, F.W. Gehring, and K.A. Ribet. It covers the theory of one-parameter semigroups of linear operators on Banach spaces, starting with the Hille–Yosida generation theorem and progressing to advanced topics such as spectral theory, perturbation theory, and applications to various evolution equations. The authors emphasize the importance of strongly continuous semigroups and provide a comprehensive treatment of related concepts, including interpolation and extrapolation spaces, perturbation theorems, and approximation formulas. The book also includes historical perspectives and philosophical discussions on the relationship between semigroups and evolution equations, as well as determinism. The preface highlights the book's structure, intended audience, and contributions from various experts in the field.
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