A Course in Functional Analysis and Measure Theory (Universitext)

December 8, 2020
A Course in Functional Analysis and Measure Theory (Universitext)

Provides necessary preliminariesExplores basic and advanced material in functional analysis andoperator theory, including applications to Fourier series and theFourier transformIncludes over 1500 exercises——————————Written by an expert on the topic and experienced lecturer, thistextbook provides an elegant, self-contained introduction tofunctional analysis, including several advanced topics andapplications to harmonic analysis.Starting from basic topics before proceeding to more advancedmaterial, the book covers measure and integration theory, classicalBanach and Hilbert space theory, spectral theory for boundedoperators, fixed point theory, Schauder bases, the Riesz-Thorininterpolation theorem for operators, as well as topics in dualityand convexity theory.Aimed at advanced undergraduate and graduate students, this bookis suitable for both introductory and more advanced courses infunctional analysis. Including over 1500 exercises of varyingdifficulty and various motivational and historical remarks, thebook can be used for self-study and alongside lecture courses.