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Harmonic and geometric analysis

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...

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Detalles Bibliográficos
Autores principales: Citti, Giovanna, Grafakos, Loukas, Pérez, Carlos, Sarti, Alessandro, Zhong, Xiao
Lenguaje:eng
Publicado: Springer 2015
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-0348-0408-0
http://cds.cern.ch/record/2015345
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author Citti, Giovanna
Grafakos, Loukas
Pérez, Carlos
Sarti, Alessandro
Zhong, Xiao
author_facet Citti, Giovanna
Grafakos, Loukas
Pérez, Carlos
Sarti, Alessandro
Zhong, Xiao
author_sort Citti, Giovanna
collection CERN
description 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.
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institution Organización Europea para la Investigación Nuclear
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publishDate 2015
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spelling cern-20153452021-04-21T20:19:15Zdoi:10.1007/978-3-0348-0408-0http://cds.cern.ch/record/2015345engCitti, GiovannaGrafakos, LoukasPérez, CarlosSarti, AlessandroZhong, XiaoHarmonic and geometric analysisMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:20153452015
spellingShingle Mathematical Physics and Mathematics
Citti, Giovanna
Grafakos, Loukas
Pérez, Carlos
Sarti, Alessandro
Zhong, Xiao
Harmonic and geometric analysis
title Harmonic and geometric analysis
title_full Harmonic and geometric analysis
title_fullStr Harmonic and geometric analysis
title_full_unstemmed Harmonic and geometric analysis
title_short Harmonic and geometric analysis
title_sort harmonic and geometric analysis
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-0348-0408-0
http://cds.cern.ch/record/2015345
work_keys_str_mv AT cittigiovanna harmonicandgeometricanalysis
AT grafakosloukas harmonicandgeometricanalysis
AT perezcarlos harmonicandgeometricanalysis
AT sartialessandro harmonicandgeometricanalysis
AT zhongxiao harmonicandgeometricanalysis