Guide to Spectral Theory

Christophe Cheverry is a mathematics professor at the University of Rennes 1. He works in the area of analysis, partial differential equations, and mathematical physics. Nicolas Raymond is a mathematics professor at the University of Angers. His research is focused on semiclassical spectral theory and partial differential equations.

• Foreword.- Prolegomena.- Chapter 1: A First Look at Spectral Theory.- Chapter 2: Unbounded Operators.- Chapter 3: Spectrum .- Chapter 4: Compact Operators.- Chapter 5: Fredholm Theory.- Chapter 6:Spectrum of Self-Adjoint Operators.- Chapter 7: Hille-Yosida and Stone’s Theorems.- Chapter 8: About the Spectral Measure.- Chapter 9: Trace-class and Hilbert-Schmidt Operators.- Chapter 10: Selected Applications of the Functional Calculus.- Appendix A: Reminders of Functional Analysis.- Bibliography.- Index.

“Throughout the text there are numerous exercises, often with complete solutions or helpful hints … . The brief notes at the end of each chapter provide useful additional comments and references to the literature. Overall, this is an interesting and engagingly written text on spectral theory and its applications. Readers with the requisite background knowledge will find in this book a wealth of interesting applications of classical spectral theory, often to problems of current interest in research.” (David Seifert, zbMATH 1505.47001, 2023)