Geometric harmonic analysis. IV, Boundary layer potentials in uniformly rectifiable domains, and applications to complex analysis / Dorina Mitrea, Irina Mitrea, Marius Mitrea.
2023
QA312
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Title
Geometric harmonic analysis. IV, Boundary layer potentials in uniformly rectifiable domains, and applications to complex analysis / Dorina Mitrea, Irina Mitrea, Marius Mitrea.
ISBN
9783031291791 (electronic bk.)
3031291794 (electronic bk.)
3031291786
9783031291784
3031291794 (electronic bk.)
3031291786
9783031291784
Published
Cham : Springer, [2023]
Copyright
©2023
Language
English
Description
1 online resource (xix, 992 pages).
Item Number
10.1007/978-3-031-29179-1 doi
Call Number
QA312
Dewey Decimal Classification
515/.42
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. Traditionally, the label Caldern-Zygmund theory has been applied to a distinguished body of works primarily pertaining to the mapping properties of singular integral operators on Lebesgue spaces, in various geometric settings. Volume IV amounts to a versatile Caldern-Zygmund theory for singular integral operators of layer potential type in open sets with uniformly rectifiable boundaries, considered on a diverse range of function spaces. Novel applications to complex analysis in several variables are also explored here.
Bibliography, etc. Note
Includes bibliographical references and indexes.
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Access limited to authorized users.
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Description based on print version record.
Added Author
Mitrea, Irina, author.
Mitrea, Marius, author.
Mitrea, Marius, author.
Series
Developments in mathematics ; v. 75.
Available in Other Form
GEOMETRIC HARMONIC ANALYSIS IV.
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Table of Contents
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.
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.