This is the fourth and final volume in the Princeton Lectures in
Analysis, a series of textbooks that aim to present, in an integrated
manner, the core areas of analysis. Beginning with the basic facts of
functional analysis, this volume looks at Banach spaces, Lp spaces,
and distribution theory, and highlights their roles in harmonic
analysis. The authors then use the Baire category theorem to illustrate
several points, including the existence of Besicovitch sets. The second
half of the book introduces readers to other central topics in analysis,
such as probability theory and Brownian motion, which culminates in the
solution of Dirichlet's problem. The concluding chapters explore several
complex variables and oscillatory integrals in Fourier analysis, and
illustrate applications to such diverse areas as nonlinear dispersion
equations and the problem of counting lattice points. Throughout the
book, the authors focus on key results in each area and stress the
organic unity of the subject.
- A comprehensive and authoritative text that treats some of the main
topics of modern analysis
- A look at basic functional analysis and its applications in harmonic
analysis, probability theory, and several complex variables
- Key results in each area discussed in relation to other areas of
mathematics
- Highlights the organic unity of large areas of analysis traditionally
split into subfields
- Interesting exercises and problems illustrate ideas
- Clear proofs provided
