Geometric Harmonic Analysis Iv
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Geometric Harmonic Analysis Iv
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Author : Dorina Mitrea
language : en
Publisher: Springer Nature
Release Date : 2023-07-09
Geometric Harmonic Analysis Iv written by Dorina Mitrea and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-09 with Mathematics categories.
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.
Geometric Harmonic Analysis V
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Author : Dorina Mitrea
language : en
Publisher: Springer Nature
Release Date : 2023-08-22
Geometric Harmonic Analysis V written by Dorina Mitrea and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-22 with Mathematics categories.
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. The ultimate goal in Volume V is to prove well-posedness and Fredholm solvability results concerning boundary value problems for elliptic second-order homogeneous constant (complex) coefficient systems, and domains of a rather general geometric nature. The formulation of the boundary value problems treated here is optimal from a multitude of points of view, having to do with geometry, functional analysis (through the consideration of a large variety of scales of function spaces), topology, and partial differential equations.
Harmonic And Geometric Analysis
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Author : Giovanna Citti
language : en
Publisher: Birkhäuser
Release Date : 2015-04-28
Harmonic And Geometric Analysis written by Giovanna Citti and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-28 with Mathematics categories.
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.
Geometric Harmonic Analysis Ii
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Author : Dorina Mitrea
language : en
Publisher: Springer Nature
Release Date : 2023-03-03
Geometric Harmonic Analysis Ii written by Dorina Mitrea and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-03 with Mathematics categories.
This monograph is part of a larger program, materializing in five volumes, whose principal 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. Volume II is concerned with function spaces measuring size and/or smoothness, such as Hardy spaces, Besov spaces, Triebel-Lizorkin spaces, Sobolev spaces, Morrey spaces, Morrey-Campanato spaces, spaces of functions of Bounded Mean Oscillations, etc., in general geometric settings. Work here also highlights the close interplay between differentiability properties of functions and singular integral operators. The text is intended for researchers, graduate students, and industry professionals interested in harmonic analysis, functional analysis, geometric measure theory, and function space theory.
Geometric Harmonic Analysis Iii
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Author : Dorina Mitrea
language : en
Publisher: Springer Nature
Release Date : 2023-05-12
Geometric Harmonic Analysis Iii written by Dorina Mitrea and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-12 with Mathematics categories.
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. Volume III is concerned with integral representation formulas for nullsolutions of elliptic PDEs, Calderón-Zygmund theory for singular integral operators, Fatou type theorems for systems of elliptic PDEs, and applications to acoustic and electromagnetic scattering. Overall, this amounts to a powerful and nuanced theory developed on uniformly rectifiable sets, which builds on the work of many predecessors.
Commutative Harmonic Analysis Iv
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Author : V.P. Khavin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Commutative Harmonic Analysis Iv written by V.P. Khavin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
With the groundwork laid in the first volume (EMS 15) of the Commutative Harmonic Analysis subseries of the Encyclopaedia, the present volume takes up four advanced topics in the subject: Littlewood-Paley theory for singular integrals, exceptional sets, multiple Fourier series and multiple Fourier integrals.
Geometric Aspects Of Harmonic Analysis
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Author : Paolo Ciatti
language : en
Publisher: Springer
Release Date : 2022-09-29
Geometric Aspects Of Harmonic Analysis written by Paolo Ciatti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-29 with Mathematics categories.
This volume originated in talks given in Cortona at the conference "Geometric aspects of harmonic analysis" held in honor of the 70th birthday of Fulvio Ricci. It presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest mathematicians working in these areas. The subjects dealt with are topics of current interest in closely interrelated areas of Fourier analysis, singular integral operators, oscillatory integral operators, partial differential equations, multilinear harmonic analysis, and several complex variables. The work is addressed to researchers in the field.
Geometric Harmonic Analysis I
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Author : Dorina Mitrea
language : en
Publisher:
Release Date : 2022
Geometric Harmonic Analysis I written by Dorina Mitrea and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
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. Volume I establishes a sharp version of the Divergence Theorem (aka Fundamental Theorem of Calculus) which allows for an inclusive class of vector fields whose boundary trace is only assumed to exist in a nontangential pointwise sense.
Harmonic Analysis And Boundary Value Problems
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Author : Luca Capogna
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Harmonic Analysis And Boundary Value Problems written by Luca Capogna and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This volume presents research and expository articles by the participants of the 25th Arkansas Spring Lecture Series on ``Recent Progress in the Study of Harmonic Measure from a Geometric and Analytic Point of View'' held at the University of Arkansas (Fayetteville). Papers in this volume provide clear and concise presentations of many problems that are at the forefront of harmonic analysis and partial differential equations. The following topics are featured: the solution of the Kato conjecture, the ``two bricks'' problem, new results on Cauchy integrals on non-smooth curves, the Neumann problem for sub-Laplacians, and a new general approach to both divergence and nondivergence second order parabolic equations based on growth theorems. The articles in this volume offer both students and researchers a comprehensive volume of current results in the field.
Harmonic Analysis And Applications
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Author : Carlos E. Kenig
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-12-14
Harmonic Analysis And Applications written by Carlos E. Kenig and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-14 with Education categories.
The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.