Bøger af Alberto Torchinsky

A modern introduction to the theory of real variables and its applications to all areas of analysis and partial differential equations. The book discusses the foundations of analysis, including the theory of integration, the Lebesque and abstract integrals, the Radon-Nikodym Theorem, the Theory of Banach and Hilbert spaces, and a glimpse of Fourier series. All material is presented in a clear and motivational fashion.

Cardinal NumbersOrdinal NumbersThe Riemann-Stieltjes IntegralAbstract MeasuresThe Lebesgue MeasureMeasurable FunctionsIntegrationMore about L1Borel MeasuresAbsolute ContinuitySigned MeasuresLp SpacesFubinis TheoremNormed Spaces and FunctionalsThe Basic PrinciplesHilbert SpacesFourier SeriesRemarks on Problems and Questions

This text starts with Fourier series, summability, norm convergence, and conjugate function. Additional topics include Hilbert transform, Paley theory, Cauchy integrals on Lipschitz curves, and boundary value problems. 1986 edition.