Geometric Harmonic Analysis I

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 1006 pages
File Size : 48,7 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.

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 940 pages
File Size : 48,7 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.

Author : Paolo Ciatti,Alessio Martini
Publisher : Springer Nature
Page : 488 pages
File Size : 46,5 Mb
Release : 2021-09-27
Category : Mathematics
ISBN : 9783030720582

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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.

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 938 pages
File Size : 46,9 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.

Author : Dorina Mitrea,Marius Mitrea
Publisher : Unknown
Page : 0 pages
File Size : 52,5 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.

Author : Giovanna Citti,Loukas Grafakos,Carlos Pérez,Alessandro Sarti,Xiao Zhong
Publisher : Birkhäuser
Page : 170 pages
File Size : 44,7 Mb
Release : 2015-04-28
Category : Mathematics
ISBN : 9783034804080

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Harmonic and Geometric Analysis by Giovanna Citti,Loukas Grafakos,Carlos Pérez,Alessandro Sarti,Xiao Zhong Pdf

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.

Author : Massimo Picardello
Publisher : CRC Press
Page : 194 pages
File Size : 50,7 Mb
Release : 2019-04-15
Category : Mathematics
ISBN : 9780429530319

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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

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 1004 pages
File Size : 42,5 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.

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 980 pages
File Size : 54,5 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.

Author : Akram Aldroubi,Carlos Cabrelli,Stéphane Jaffard,Ursula Molter
Publisher : Springer Nature
Page : 335 pages
File Size : 50,7 Mb
Release : 2019-11-26
Category : Mathematics
ISBN : 9783030323530

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New Trends in Applied Harmonic Analysis, Volume 2 by Akram Aldroubi,Carlos Cabrelli,Stéphane Jaffard,Ursula Molter Pdf

This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include: Gabor frames Falconer distance problem Hausdorff dimension Sparse inequalities Fractional Brownian motion Fourier analysis in geometric measure theory This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.

Author : Ali Baklouti,Takaaki Nomura
Publisher : Springer Nature
Page : 217 pages
File Size : 42,9 Mb
Release : 2019-08-31
Category : Mathematics
ISBN : 9783030265625

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Geometric and Harmonic Analysis on Homogeneous Spaces by Ali Baklouti,Takaaki Nomura Pdf

This book presents a number of important contributions focusing on harmonic analysis and representation theory of Lie groups. All were originally presented at the 5th Tunisian–Japanese conference “Geometric and Harmonic Analysis on Homogeneous Spaces and Applications”, which was held at Mahdia in Tunisia from 17 to 21 December 2017 and was dedicated to the memory of the brilliant Tunisian mathematician Majdi Ben Halima. The peer-reviewed contributions selected for publication have been modified and are, without exception, of a standard equivalent to that in leading mathematical periodicals. Highlighting the close links between group representation theory and harmonic analysis on homogeneous spaces and numerous mathematical areas, such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations and mathematical physics, the book is intended for researchers and students working in the area of commutative and non-commutative harmonic analysis as well as group representations.

Author : Alexander Koldobsky,Vladyslav Yaskin
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 44,8 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 0821883356

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The Interface Between Convex Geometry and Harmonic Analysis by Alexander Koldobsky,Vladyslav Yaskin Pdf

"The book is written in the form of lectures accessible to graduate students. This approach allows the reader to clearly see the main ideas behind the method, rather than to dwell on technical difficulties. The book also contains discussions of the most recent advances in the subject. The first section of each lecture is a snapshot of that lecture. By reading each of these sections first, novices can gain an overview of the subject, then return to the full text for more details."--BOOK JACKET.

Author : N.E. Hurt
Publisher : Springer Science & Business Media
Page : 362 pages
File Size : 40,8 Mb
Release : 1982-12-31
Category : Mathematics
ISBN : 9027714266

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Geometric Quantization in Action by N.E. Hurt Pdf

Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will fmd the final question. G. K. Chesterton, The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geo metry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical progmmming profit from homotopy theory; Lie algebras are relevant to fIltering; and prediction and electrical engineering can use Stein spaces.

Author : Massimo Picardello
Publisher : Unknown
Page : 128 pages
File Size : 53,8 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 1138441740

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Harmonic Analysis and Integral Geometry by Massimo Picardello Pdf

Author : Eric Grinberg
Publisher : American Mathematical Soc.
Page : 180 pages
File Size : 50,8 Mb
Release : 1992
Category : Mathematics
ISBN : 0821854755

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Geometric Analysis by Eric Grinberg Pdf

This volume contains the refereed proceedings of the Special Session on Geometric Analysis held at the AMS meeting in Philadelphia in October 1991. The term ''geometric analysis'' is being used with increasing frequency in the mathematical community, but its meaning is not entirely fixed. The papers in this collection should help to better define the notion of geometric analysis by illustrating emerging trends in the subject. The topics covered range over a broad spectrum: integral geometry, Radon transforms, geometric inequalities, microlocal analysis, harmonic analysis, analysis on Lie groups and symmetric spaces, and more. Containing articles varying from the expository to the technical, this book presents the latest results in a broad range of analytic and geometric topics.