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Geometric Harmonic Analysis I
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Geometric Harmonic Analysis I : A Sharp Divergence Theorem with Nontangential Pointwise Traces

2022 ed.

by Dorina Mitrea , Irina Mitrea , Marius Mitrea

Book Details

Format Hardback or Cased Book
Book Series Developments in Mathematics
ISBN-10 3031059492
ISBN-13 9783031059490
Edition 2022 ed.
Publisher Springer International Publishing AG
Imprint Springer International Publishing AG
Country of Manufacture GB
Country of Publication GB
Publication Date Nov 5th, 2022
Print length 924 Pages
Product Classification: Complex analysis, complex variables Functional analysis & transforms
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This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Volume I establishes a sharp version of the Divergence Theorem (aka Fundamental Theorem of Calculus) which allows for an inclusive class of vector fields whose boundary trace is only assumed to exist in a nontangential pointwise sense.
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations.

Volume I establishes a sharp version of the Divergence Theorem (aka Fundamental Theorem of Calculus) which allows for an inclusive class of vector fields whose boundary trace is only assumed to exist in a nontangential pointwise sense.

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