A Guide to Spectral Theory: Applications and Exercises

This textbook provides a comprehensive introduction to the spectral theory of linear operators on Banach and Hilbert spaces, covering key components and applications in quantum physics. It is designed for graduate students and researchers, with a focus on detailed proofs and examples.

Format: Paperback / softback
Length: 258 pages
Publication date: 07 May 2022
Publisher: Springer Nature Switzerland AG

This comprehensive textbook offers a thorough graduate-level exploration into the spectral theory of linear operators on Banach and Hilbert spaces. Authored by experienced educators, it guides readers through essential aspects of spectral theory and its applications in quantum physics, presenting topics in a progressive manner that builds upon previous chapters. Researchers and students alike will benefit from the exploration of advanced applications and research perspectives presented towards the end of the book.

The text begins with a brief introduction to the relationship between spectral theory and quantum physics, setting the stage for the subsequent chapters. It then delves into the study of unbounded operators, analyzing closed, adjoint, and self-adjoint operators. The spectrum of a closed operator is defined, and fundamental properties of Fredholm operators are introduced. The authors employ the Grushin method to perform spectral analysis of compact operators, a crucial tool in this field.

Subsequent chapters focus on examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. Detailed proofs are provided throughout, accompanied by illustrative examples to enhance understanding. In the final chapter, the discussion extends to several selected applications, showcasing the practical applications of spectral theory.

Designed for graduate students enrolled in an introductory course in spectral theory or operator theory, A Guide to Spectral Theory: Applications and Exercises assumes a foundational understanding of linear functional analysis and partial differential equations. While basic knowledge of bounded linear operators is useful, it is not mandatory. PhD students and researchers in the field of mathematics and physics will find this textbook an invaluable resource for advancing their knowledge and understanding of spectral theory.

Weight: 433g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030674649
Edition number: 1st ed. 2021