Harmonic Analysis Techniques for Elliptic Operators

Name: Harmonic Analysis Techniques for Elliptic Operators
Price: 208.75 AUD
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Lecture Notes of the 27th Internet Seminar on Evolution Equations

By: Moritz Egert, Sylvie Monniaux, Robert Haller, Patrick Tolksdorf

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Hardcover | 23 June 2026

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Hardcover

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23.5 x 15.5

Hardcover

$208.75

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Available: 23rd June 2026

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The study of the Laplacian through the Fourier transform lies at the center of classical harmonic analysis. It is Plancherelâs theorem that intimately links square-integrable functions with the theory of weak derivatives and a symbolic calculus for the Laplacian. Examples include Littlewoodâ"Paley inequalities, Riesz transform estimates and Calder³nâ"Zygmund extrapolation. Over the last decades, the quest to generalize these properties to elliptic operators L in divergence form with bounded measurable coefficients has triggered the development of new techniques that led to a surge of spectacular results in elliptic and parabolic PDE theory. Assuming only undergraduate knowledge in analysis and some background on Hilbert spaces and the Fourier transform, the authors develop the cornerstones of this âL-adapted Fourier analysisâ over 14 consecutive lectures. As they delve deeper into the topic, readers make first encounters with maximal functions, Carleson measures and a T(b) theorem. The lectures culminate in a self-contained presentation of the solution to the Kato conjecture, a challenging problem that resisted solution for 40 years until it was finally solved in 2001. This book can serve as a fully developed curriculum for a first graduate course in harmonic analysis and PDEs. Based on the 27th Internet Seminar on Evolution Equations, organized by the authors in the 2023/24 academic year, each lecture is enriched with original exercises, detailed solutions, and video presentations guiding through each theoremâs proof and offering additional insights.

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