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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
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Fourier Restriction, Decoupling, and Applications (Hardcover)
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Fourier Restriction, Decoupling, and Applications (Hardcover)
Series: Cambridge Studies in Advanced Mathematics
Expected to ship within 12 - 17 working days
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The last fifteen years have seen a flurry of exciting developments
in Fourier restriction theory, leading to significant new
applications in diverse fields. This timely text brings the reader
from the classical results to state-of-the-art advances in
multilinear restriction theory, the Bourgain-Guth induction on
scales and the polynomial method. Also discussed in the second part
are decoupling for curved manifolds and a wide variety of
applications in geometric analysis, PDEs (Strichartz estimates on
tori, local smoothing for the wave equation) and number theory
(exponential sum estimates and the proof of the Main Conjecture for
Vinogradov's Mean Value Theorem). More than 100 exercises in the
text help reinforce these important but often difficult ideas,
making it suitable for graduate students as well as specialists.
Written by an author at the forefront of the modern theory, this
book will be of interest to everybody working in harmonic analysis.
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