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Functional Analysis - Introduction to Further Topics in Analysis (Hardcover)
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Functional Analysis - Introduction to Further Topics in Analysis (Hardcover)
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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
General
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