Operator theory
Operator theory
About this book
A Comprehensive Course in Analysis by Poincaré 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.
Details
- OL Work ID
- OL22320448W
Subjects
Functional analysis -- Topological algebras, normed rings and algebras, Banach algebras -- General theory of topological algebrasOrdinary differential equations -- Instructional exposition (textbooks, tutorial papers, etc.).TextbooksOrdinary differential equations -- Ordinary differential operators -- General spectral theoryPartial differential equations -- Spectral theory and eigenvalue problems -- General topics in linear spectral theoryMathematical analysisFunctional analysis -- Instructional exposition (textbooks, tutorial papers, etc.).Quantum theory -- General mathematical topics and methods in quantum theory -- Selfadjoint operator theory in quantum theory, including spectral analysisOperator theory -- Instructional exposition (textbooks, tutorial papers, etc.).Topological groups, Lie groups -- Locally compact abelian groups (LCA groups) -- General properties and structure of LCA groupsHarmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Orthogonal functions and polynomials, general theoryOperator theory