EAN: 9783030674649

A GUIDE TO SPECTRAL THEORY - CHRISTOPHE CHEVERR...

This textbook provides a graduate-level introduction to the spectral theory of linear operators
on Banach and Hilbert spaces  guiding readers through key components of spectral theory and its
applications in quantum physics. Based on their extensive teaching experience  the authors
present topics in a progressive manner so that each chapter builds on the ones preceding.
Researchers and students alike will also appreciate the exploration of more advanced
applications and research perspectives presented near the end of the book.Beginning with a
brief introduction to the relationship between spectral theory and quantum physics  the authors
go on to explore unbounded operators  analyzing closed  adjoint  and self-adjoint operators.
Next  the spectrum of a closed operator is defined and the fundamental properties of Fredholm
operators are introduced. The authors then develop the Grushin method to execute the spectral
analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida
and Stone theorems  the spectral analysis of self-adjoint operators  and trace-class and
Hilbert-Schmidt operators. The final chapter opens the discussion to several selected
applications. Throughout this textbook  detailed proofs are given  and the statements are
illustrated by a number of well-chosen examples. At the end  an appendix about foundational
functional analysis theorems is provided to help the uninitiated reader.A Guide to Spectral
Theory: Applications and Exercises is intended for graduate students taking an introductory
course in spectral theory or operator theory. A background in linear functional analysis and
partial differential equations is assumed  basic knowledge of bounded linear operators is
useful but not required. PhD students and researchers will also find this volume to be of
interest  particularly the research directions provided in later chapters.

Aktuelle Preise zur EAN 9783030674649

Produktinformationen zur 9783030674649