Schnaubelt R. Spectral Theory 2025

Textbook in PDF format

General spectral theory
Closed operators
The spectrum
Spectral theory of compact operators
Compact operators
The Fredholm alternative
Closed operators with compact resolvent
Fredholm operators and the essential spectrum
Appendix: The Dirichlet problem and boundary integrals
Fourier transform, Sobolev spaces, and weak derivatives
The Fourier transform
Basic properties of Sobolev spaces
Main results on Sobolev spaces
Differential operators in Lp -spaces
Appendix: Density, embedding and trace theorems
Appendix: Tempered distributions
Self-adjoint operators
Basic properties
The spectral theorems
Holomorphic functional calculi
The bounded case
Sectorial operators
Bibliography