Harmonic analysis
Harmonic analysis
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 3 returns to the themes of Part 1 by discussing pointwise limits (going beyond the usual focus on the Hardy-Littlewood maximal function by including ergodic theorems and martingale convergence), harmonic functions and potential theory, frames and wavelets, spaces (including bounded mean oscillation (BMO)) and, in the final chapter, lots of inequalities, including Sobolev spaces, Calderon-Zygmund estimates, and hypercontractive semigroups.
Details
- OL Work ID
- OL22318446W
Subjects
Real functions -- Instructional exposition (textbooks, tutorial papers, etc.).Functions of a complex variable -- Spaces and algebras of analytic functions -- Hardy spacesHarmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Wavelets and other special systemsTextbooksHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Calderón-Zygmund, etc.).Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.).Harmonic analysisFunctions of a complex variable -- Spaces and algebras of analytic functions -- BMO-spacesFunctional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theoremsPotential theory -- Instructional exposition (textbooks, tutorial papers, etc.).Mathematical analysis