Geometric Harmonic Analysis IV: Boundary Layer Potentials in Uniformly Rectifiable Domains, and Applications to Complex Analysis - Couverture rigide

Mitrea, Dorina; Mitrea, Irina; Mitrea, Marius

Couverture rigide

ISBN 10 : 3031291786 ISBN 13 : 9783031291784

Editeur : Springer International Publishing AG, 2023

Synopsis

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 “Calderón-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 Calderón-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.

A propos du livre

À propos de l'auteur

Dorina Mitrea, Irina Mitrea, Marius Mitrea, and Joel Shapiro are internationally recognized mathematicians with expertise spanning across the fields of Harmonic Analysis, Functional Analysis, and Partial Differential Equations. Dorina Mitrea, Irina Mitrea, and Marius Mitrea are Fellows of the American Mathematical Society and have collaborated extensively over the years. Their joint contributions include over a dozen of original research monographs, notably the comprehensive five-volume series Geometric Harmonic Analysis (Springer), The Hodge-Laplacian, now in its second edition (De Gruyter), Singular Integral Operators, Quantitative Flatness, and Boundary Problems (Birkhauser), Groupoid Metrization Theory (Birkhauser). Their work has significantly impacted harmonic analysis of geometric flavor. Joel Shapiro is a distinguished scholar renowned for his pioneering research in the topological and geometric aspects of functional analysis, particularly composition operators.

Traditionally, the label "Calderón-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 Calderón-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.

Détails de l'édition

• Éditeur: Springer International Publishing AG
• Date d'édition: 2023
• Langue: anglais
• ISBN 10: 3031291786
• ISBN 13: 9783031291784
• Reliure: Relié
• Nombre de pages: 992
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne