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Title
Geometric harmonic analysis. III, Integral representations, Calderón-Zygmund theory, Fatou theorems, and applications to scattering / Dorina Mitrea, Irina Mitrea, Marius Mitrea.
ISBN
9783031227356 (electronic bk.)
3031227352 (electronic bk.)
9783031227349
3031227344
Published
Cham : Springer, 2023.
Language
English
Description
1 online resource (972 pages) : illustrations (colour).
Item Number
10.1007/978-3-031-22735-6 doi
Call Number
QA433
Dewey Decimal Classification
515.4
Summary
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 III is concerned with integral representation formulas for nullsolutions of elliptic PDEs, Caldern-Zygmund theory for singular integral operators, Fatou type theorems for systems of elliptic PDEs, and applications to acoustic and electromagnetic scattering. Overall, this amounts to a powerful and nuanced theory developed on uniformly rectifiable sets, which builds on the work of many predecessors.
Bibliography, etc. Note
Includes bibliographical references and indexes.
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Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Developments in mathematics ; v. 74.
Introduction and Statement of Main Results Concerning the Divergence Theorem
Examples, Counterexamples, and Additional Perspectives
Tools from Geometric Measure Theory, Harmonic Analysis, and functional Analysis
Open Sets with Locally Finite Surface Measures and Boundary Behavior
Proofs of the Main Results Pertaining to the Divergence Theorem
Applications to Singular Integrals, Function Spaces, Boundary Problems, and Further Results.