Del 273 - Operator Theory: Advances and Applications

Gibbs Semigroups

Inbunden, Engelska, 2019

AvValentin A. Zagrebnov

1 129 kr

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This book focuses on the theory of the Gibbs semigroups, which originated in the 1970s and was motivated by the study of strongly continuous operator semigroups with values in the trace-class ideal. The book offers an up-to-date, exhaustive overview of the advances achieved in this theory after half a century of development. It begins with a tutorial introduction to the necessary background material, before presenting the Gibbs semigroups and then providing detailed and systematic information on the Trotter-Kato product formulae in the trace-norm topology. In addition to reviewing the state-of-art concerning the Trotter-Kato product formulae, the book extends the scope of exposition from the trace-class ideal to other ideals. Here, special attention is paid to results on semigroups in symmetrically normed ideals and in the Dixmier ideal.By examining the progress made in Gibbs semigroup theory and in extensions of the Trotter-Kato product formulae to symmetrically normed and Dixmier ideals, the book shares timely and valuable insights for readers interested in pursuing these subjects further. As such, it will appeal to researchers, undergraduate and graduate students in mathematics and mathematical physics.

Produktinformation

Utgivningsdatum2019-11-27
Mått155 x 235 x 24 mm
Vikt670 g
FormatInbunden
SpråkEngelska
SerieOperator Theory: Advances and Applications
Antal sidor320
FörlagSpringer Nature Switzerland AG
ISBN9783030188764

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Beräkning och matematisk analys inom Naturvetenskap och teknik

Semigroups and their generators.- Classes of compact operators.- Trace inequalities.- Gibbs semigroups.- Product formulae for Gibbs semigroups.- Product formulae in symmetrically-normed ideals.- Product formulae in Dixmier ideal.- Appendix A. Spectra of closed operators.- Appendix B. Inequalities in ideals.- Appendix B. More inequalities.- Appendix C. Kato functions.- Appendix D. Lie-Trotter-Kato product formulae: comments on the bibliography.- Bibliography.- Index

“This well-written and organized book is a reader-friendly manual in the field of Gibbs semigroups. It can be recommended for experts and graduate, postgraduate, and doctoral students.” (Michael Perelmuter, zbMATH 1512.47004, 2023)“The book captures a fascinating snapshot of the current state of Gibbs semigroup theory. The book also provides references to the rich literature, nice historical remarks, and inspiring comments on the topics. It is readable and appropriate for readers who are familiar with the basics of functional analysis and linear operator theory. As such, the book will appeal to students at the senior undergraduate and graduate levels as well as researchers in mathematics and mathematical physics.” (Min He, Mathematical Reviews, June, 2021)