Harmonic and Geometric Analysis

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Beschreibung

This volume contains two surveys of new results on linear and multilinear analysis. It offers an insightful presentation of the De Giorgi-Moser-Nash result and contains elegant applications of harmonic analysis to human vision.

This book contains an expanded version of lectures delivered by the authors at the CRM in Spring of 2009. It contains four series of lectures. The first one is an application of harmonic analysis and the Heisenberg group to understand human vision. The second and third series of lectures cover some of the main topics on linear and multilinear harmonic analysis. The last one is a clear introduction to a deep result of De Giorgi, Moser and Nash on regularity of elliptic partial differential equations in divergence form.

Klappentext

This book presents an expanded version of four series of lectures delivered by the authors at the CRM.

Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the CalderónZygmund theory, especially the Lp inequalities for CalderónZygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights.

The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differential equations in divergence form.



Inhalt

1 Models of the Visual Cortex in Lie Groups.- 2 Multilinear CalderónZygmund Singular Integrals.- 3 Singular Integrals and Weights.- 4 De GiorgiNashMoser Theory.

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Produktinformationen

Titel
Harmonic and Geometric Analysis
Autor
Editor
EAN
9783034804073
ISBN
978-3-0348-0407-3
Format
Kartonierter Einband
Genre
Mathematik
Anzahl Seiten
170
Gewicht
365g
Größe
H9mm x B245mm x T170mm
Jahr
2015
Untertitel
Englisch
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