Geometric Harmonic Analysis Iv

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Geometric Harmonic Analysis IV

Dorina Mitrea,Irina Mitrea,Marius Mitrea
Geometric Harmonic Analysis IV Book PDF

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 1004 pages
File Size : 51,8 Mb
Release : 2023-07-09
Category : Mathematics
ISBN : 9783031291791

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Geometric Harmonic Analysis IV by Dorina Mitrea,Irina Mitrea,Marius Mitrea Pdf

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

Dorina Mitrea,Irina Mitrea,Marius Mitrea
Geometric Harmonic Analysis V Book PDF

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 1006 pages
File Size : 41,9 Mb
Release : 2023-08-22
Category : Mathematics
ISBN : 9783031315619

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Geometric Harmonic Analysis V by Dorina Mitrea,Irina Mitrea,Marius Mitrea Pdf

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.

Geometric Harmonic Analysis II

Dorina Mitrea,Irina Mitrea,Marius Mitrea
Geometric Harmonic Analysis II Book PDF

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 938 pages
File Size : 54,7 Mb
Release : 2023-03-03
Category : Mathematics
ISBN : 9783031137181

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Geometric Harmonic Analysis II by Dorina Mitrea,Irina Mitrea,Marius Mitrea Pdf

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 I

Dorina Mitrea,Irina Mitrea,Marius Mitrea
Geometric Harmonic Analysis I Book PDF

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 940 pages
File Size : 54,7 Mb
Release : 2022-11-04
Category : Mathematics
ISBN : 9783031059506

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Geometric Harmonic Analysis I by Dorina Mitrea,Irina Mitrea,Marius Mitrea Pdf

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.

Geometric Harmonic Analysis III

Dorina Mitrea,Irina Mitrea,Marius Mitrea
Geometric Harmonic Analysis III Book PDF

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 980 pages
File Size : 51,6 Mb
Release : 2023-05-12
Category : Mathematics
ISBN : 9783031227356

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Geometric Harmonic Analysis III by Dorina Mitrea,Irina Mitrea,Marius Mitrea Pdf

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

V.P. Khavin,N.K. Nikol'skii
Commutative Harmonic Analysis IV Book PDF

Author : V.P. Khavin,N.K. Nikol'skii
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 55,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662063019

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Commutative Harmonic Analysis IV by V.P. Khavin,N.K. Nikol'skii Pdf

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 Harmonic Analysis I

Dorina Mitrea,Irina Mitrea,Marius Mitrea
Geometric Harmonic Analysis I Book PDF

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Unknown
Page : 0 pages
File Size : 53,8 Mb
Release : 2022
Category : Electronic
ISBN : 3031059514

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Geometric Harmonic Analysis I by Dorina Mitrea,Irina Mitrea,Marius Mitrea Pdf

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.

Geometric and Harmonic Analysis on Homogeneous Spaces and Applications

Ali Baklouti,Hideyuki Ishi
Geometric and Harmonic Analysis on Homogeneous Spaces and Applications Book PDF

Author : Ali Baklouti,Hideyuki Ishi
Publisher : Springer Nature
Page : 268 pages
File Size : 50,7 Mb
Release : 2021-10-29
Category : Mathematics
ISBN : 9783030783464

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Geometric and Harmonic Analysis on Homogeneous Spaces and Applications by Ali Baklouti,Hideyuki Ishi Pdf

This book collects a series of important works on noncommutative harmonic analysis on homogeneous spaces and related topics. All the authors participated in the 6th Tunisian-Japanese conference "Geometric and Harmonic Analysis on homogeneous spaces and Applications" held at Djerba Island in Tunisia during the period of December 16-19, 2019. The aim of this conference and the five preceding Tunisian-Japanese meetings was to keep up with the active development of representation theory interrelated with various other mathematical fields, such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations, and mathematical physics. The present volume is dedicated to the memory of Takaaki Nomura, who organized the series of Tunisian-Japanese conferences with great effort and enthusiasm. The book is a valuable resource for researchers and students working in various areas of analysis, geometry, and algebra in connection with representation theory.

Geometric Harmonic Analysis

Dorina Mitrea,Marius Mitrea
Geometric Harmonic Analysis Book PDF

Author : Dorina Mitrea,Marius Mitrea
Publisher : Unknown
Page : 0 pages
File Size : 47,5 Mb
Release : 2022
Category : Divergence theorem
ISBN : 8303105957

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Geometric Harmonic Analysis by Dorina Mitrea,Marius Mitrea Pdf

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.

Commutative Harmonic Analysis I

V.P. Khavin,N.K. Nikol'skij
Commutative Harmonic Analysis I Book PDF

Author : V.P. Khavin,N.K. Nikol'skij
Publisher : Springer Science & Business Media
Page : 275 pages
File Size : 45,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662027325

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Commutative Harmonic Analysis I by V.P. Khavin,N.K. Nikol'skij Pdf

This volume is the first in the series devoted to the commutative harmonic analysis, a fundamental part of the contemporary mathematics. The fundamental nature of this subject, however, has been determined so long ago, that unlike in other volumes of this publication, we have to start with simple notions which have been in constant use in mathematics and physics. Planning the series as a whole, we have assumed that harmonic analysis is based on a small number of axioms, simply and clearly formulated in terms of group theory which illustrate its sources of ideas. However, our subject cannot be completely reduced to those axioms. This part of mathematics is so well developed and has so many different sides to it that no abstract scheme is able to cover its immense concreteness completely. In particular, it relates to an enormous stock of facts accumulated by the classical "trigonometric" harmonic analysis. Moreover, subjected to a general mathematical tendency of integration and diffusion of conventional intersubject borders, harmonic analysis, in its modem form, more and more rests on non-translation invariant constructions. For example, one ofthe most signifi cant achievements of latter decades, which has substantially changed the whole shape of harmonic analysis, is the penetration in this subject of subtle techniques of singular integral operators.

Harmonic Analysis and Applications

Carlos E. Kenig
Harmonic Analysis and Applications Book PDF

Author : Carlos E. Kenig
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 51,6 Mb
Release : 2020-12-14
Category : Education
ISBN : 9781470461270

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Harmonic Analysis and Applications by Carlos E. Kenig Pdf

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.

Geometric Aspects of Harmonic Analysis

Paolo Ciatti,Alessio Martini
Geometric Aspects of Harmonic Analysis Book PDF

Author : Paolo Ciatti,Alessio Martini
Publisher : Springer
Page : 479 pages
File Size : 41,9 Mb
Release : 2021-09-20
Category : Mathematics
ISBN : 3030720578

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Geometric Aspects of Harmonic Analysis by Paolo Ciatti,Alessio Martini Pdf

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.

Harmonic Analysis and Boundary Value Problems

Luca Capogna,Loredana Lanzani
Harmonic Analysis and Boundary Value Problems Book PDF

Author : Luca Capogna,Loredana Lanzani
Publisher : American Mathematical Soc.
Page : 158 pages
File Size : 42,6 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821827451

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Harmonic Analysis and Boundary Value Problems by Luca Capogna,Loredana Lanzani Pdf

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 Integral Geometry

Massimo Picardello
Harmonic Analysis and Integral Geometry Book PDF

Author : Massimo Picardello
Publisher : CRC Press
Page : 180 pages
File Size : 46,6 Mb
Release : 2019-05-08
Category : Mathematics
ISBN : 9781482285697

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Harmonic Analysis and Integral Geometry by Massimo Picardello Pdf

Comprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress. This lively and very successful event drew the attendance of many top researchers, who offered both individual lecture

Singular Integral Operators, Quantitative Flatness, and Boundary Problems

Juan José Marín,José María Martell,Dorina Mitrea,Irina Mitrea,Marius Mitrea
Singular Integral Operators Quantitative Flatness and Boundary Problems Book PDF

Author : Juan José Marín,José María Martell,Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 605 pages
File Size : 45,6 Mb
Release : 2022-09-29
Category : Mathematics
ISBN : 9783031082344

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Singular Integral Operators, Quantitative Flatness, and Boundary Problems by Juan José Marín,José María Martell,Dorina Mitrea,Irina Mitrea,Marius Mitrea Pdf

This monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many significant new results are explored in detail, with complete proofs, emphasizing and elaborating on the link between the geometric measure-theoretic features of an underlying surface and the functional analytic properties of singular integral operators defined on it. Graduate students, researchers, and professionals interested in a modern account of the topic of singular integral operators and boundary value problems – as well as those more generally interested in harmonic analysis, PDEs, and geometric analysis – will find this text to be a valuable addition to the mathematical literature.