Geometric Harmonic Analysis Iii
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Author |
: Dorina Mitrea |
Publisher |
: Springer Nature |
Total Pages |
: 980 |
Release |
: 2023-05-12 |
ISBN-10 |
: 9783031227356 |
ISBN-13 |
: 3031227352 |
Rating |
: 4/5 (56 Downloads) |
Synopsis Geometric Harmonic Analysis III by : Dorina Mitrea
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 |
: Dorina Mitrea |
Publisher |
: Springer Nature |
Total Pages |
: 1006 |
Release |
: 2023-08-22 |
ISBN-10 |
: 9783031315619 |
ISBN-13 |
: 3031315618 |
Rating |
: 4/5 (19 Downloads) |
Synopsis Geometric Harmonic Analysis V by : Dorina Mitrea
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 |
Publisher |
: Springer Nature |
Total Pages |
: 938 |
Release |
: 2023-03-03 |
ISBN-10 |
: 9783031137181 |
ISBN-13 |
: 3031137183 |
Rating |
: 4/5 (81 Downloads) |
Synopsis Geometric Harmonic Analysis II by : Dorina Mitrea
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 |
Publisher |
: Springer Nature |
Total Pages |
: 1004 |
Release |
: 2023-07-09 |
ISBN-10 |
: 9783031291791 |
ISBN-13 |
: 3031291794 |
Rating |
: 4/5 (91 Downloads) |
Synopsis Geometric Harmonic Analysis IV by : Dorina Mitrea
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 |
Publisher |
: Springer Nature |
Total Pages |
: 940 |
Release |
: 2022-11-04 |
ISBN-10 |
: 9783031059506 |
ISBN-13 |
: 3031059506 |
Rating |
: 4/5 (06 Downloads) |
Synopsis Geometric Harmonic Analysis I by : Dorina Mitrea
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 |
Publisher |
: Birkhäuser |
Total Pages |
: 178 |
Release |
: 2015-04-28 |
ISBN-10 |
: 9783034804080 |
ISBN-13 |
: 3034804083 |
Rating |
: 4/5 (80 Downloads) |
Synopsis Harmonic and Geometric Analysis by : Giovanna Citti
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 |
: Ali Baklouti |
Publisher |
: Springer Nature |
Total Pages |
: 227 |
Release |
: 2019-08-31 |
ISBN-10 |
: 9783030265625 |
ISBN-13 |
: 3030265625 |
Rating |
: 4/5 (25 Downloads) |
Synopsis Geometric and Harmonic Analysis on Homogeneous Spaces by : Ali Baklouti
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 |
: Paolo Ciatti |
Publisher |
: Springer Nature |
Total Pages |
: 488 |
Release |
: 2021-09-27 |
ISBN-10 |
: 9783030720582 |
ISBN-13 |
: 3030720586 |
Rating |
: 4/5 (82 Downloads) |
Synopsis Geometric Aspects of Harmonic Analysis by : Paolo Ciatti
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 |
: Akram Aldroubi |
Publisher |
: Springer Nature |
Total Pages |
: 335 |
Release |
: 2019-11-26 |
ISBN-10 |
: 9783030323530 |
ISBN-13 |
: 3030323536 |
Rating |
: 4/5 (30 Downloads) |
Synopsis New Trends in Applied Harmonic Analysis, Volume 2 by : Akram Aldroubi
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 |
: A.A. Kirillov |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 274 |
Release |
: 2013-03-09 |
ISBN-10 |
: 9783662097564 |
ISBN-13 |
: 3662097567 |
Rating |
: 4/5 (64 Downloads) |
Synopsis Representation Theory and Noncommutative Harmonic Analysis II by : A.A. Kirillov
Two surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.