Operator Theory: A Comprehensive Course in Analysis, Part 4
Barry Simon, "Operator Theory: A Comprehensive Course in Analysis, Part 4"
English | ISBN: 1470411032 | 2016 | 749 pages | PDF | 8 MB
English | ISBN: 1470411032 | 2016 | 749 pages | PDF | 8 MB
A Comprehensive Course in Analysis by Poincare Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis.
Part 4 focuses on operator theory, especially on a Hilbert space. Central topics are the spectral theorem, the theory of trace class and Fredholm determinants, and the study of unbounded self-adjoint operators. There is also an introduction to the theory of orthogonal polynomials and a long chapter on Banach algebras, including the commutative and non-commutative Gel'fand-Naimark theorems and Fourier analysis on general locally compact abelian groups.