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Harmonic and Geometric Analysis (Advanced Courses in Mathematics - CRM Barcelona)

De (autor) , , , , Joan Mateu
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en Limba Engleză Carte Paperback – 22 May 2015
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.
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Specificații

ISBN-13: 9783034804073
ISBN-10: 3034804075
Pagini: 190
Dimensiuni: 168 x 240 x 13 mm
Greutate: 0.37 kg
Ediția: 2015
Editura: Springer
Colecția Birkhäuser
Seria Advanced Courses in Mathematics - CRM Barcelona

Locul publicării: Basel, Switzerland

Public țintă

Graduate

Cuprins

1 Models of the Visual Cortex in Lie Groups.- 2 Multilinear Calderón–Zygmund Singular Integrals.- 3 Singular Integrals and Weights.- 4 De Giorgi–Nash–Moser Theory.

Textul de pe ultima copertă

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 Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund 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.

Caracteristici

Contains two surveys of new results on linear and multilinear analysis
Offers a very nice presentation of the De Giorgi–Moser–Nash result
Contains elegant applications of harmonic analysis to human vision