Riesz Transforms Hodge Dirac Operators And Functional Calculus For Multipliers

Author : Cédric Arhancet,Christoph Kriegler
Publisher : Springer Nature
Page : 288 pages
File Size : 44,9 Mb
Release : 2022-05-05
Category : Mathematics
ISBN : 9783030990114

Get Book

Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers by Cédric Arhancet,Christoph Kriegler Pdf

This book on recent research in noncommutative harmonic analysis treats the Lp boundedness of Riesz transforms associated with Markovian semigroups of either Fourier multipliers on non-abelian groups or Schur multipliers. The detailed study of these objects is then continued with a proof of the boundedness of the holomorphic functional calculus for Hodge–Dirac operators, thereby answering a question of Junge, Mei and Parcet, and presenting a new functional analytic approach which makes it possible to further explore the connection with noncommutative geometry. These Lp operations are then shown to yield new examples of quantum compact metric spaces and spectral triples. The theory described in this book has at its foundation one of the great discoveries in analysis of the twentieth century: the continuity of the Hilbert and Riesz transforms on Lp. In the works of Lust-Piquard (1998) and Junge, Mei and Parcet (2018), it became apparent that these Lp operations can be formulated on Lp spaces associated with groups. Continuing these lines of research, the book provides a self-contained introduction to the requisite noncommutative background. Covering an active and exciting topic which has numerous connections with recent developments in noncommutative harmonic analysis, the book will be of interest both to experts in no-commutative Lp spaces and analysts interested in the construction of Riesz transforms and Hodge–Dirac operators.

Author : John Ryan,Daniele C Struppa
Publisher : CRC Press
Page : 260 pages
File Size : 44,5 Mb
Release : 1999-01-06
Category : Mathematics
ISBN : 0582356814

Get Book

Dirac Operators in Analysis by John Ryan,Daniele C Struppa Pdf

Clifford analysis has blossomed into an increasingly relevant and fashionable area of research in mathematical analysis-it fits conveniently at the crossroads of many fundamental areas of research, including classical harmonic analysis, operator theory, and boundary behavior. This book presents a state-of-the-art account of the most recent developments in the field of Clifford analysis with contributions by many of the field's leading researchers.

Author : Tuomas Hytönen,Jan van Neerven,Mark Veraar,Lutz Weis
Publisher : Springer
Page : 616 pages
File Size : 40,6 Mb
Release : 2018-02-14
Category : Mathematics
ISBN : 9783319698083

Get Book

Analysis in Banach Spaces by Tuomas Hytönen,Jan van Neerven,Mark Veraar,Lutz Weis Pdf

This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.

Author : Anonim
Publisher : Unknown
Page : 782 pages
File Size : 54,5 Mb
Release : 2015
Category : Mathematics
ISBN : UCSD:31822041735622

Get Book

Revista Matemática Iberoamericana by Anonim Pdf

Author : Michael Stone,Paul Goldbart
Publisher : Cambridge University Press
Page : 821 pages
File Size : 40,5 Mb
Release : 2009-07-09
Category : Science
ISBN : 9781139480611

Get Book

Mathematics for Physics by Michael Stone,Paul Goldbart Pdf

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.

Author : Anonim
Publisher : Unknown
Page : 1236 pages
File Size : 42,8 Mb
Release : 1998
Category : Mathematics
ISBN : UOM:39015049327805

Get Book

Mathematical Reviews by Anonim Pdf

Author : George C. Hsiao,Wolfgang L. Wendland
Publisher : Springer Nature
Page : 783 pages
File Size : 53,9 Mb
Release : 2021-03-26
Category : Mathematics
ISBN : 9783030711276

Get Book

Boundary Integral Equations by George C. Hsiao,Wolfgang L. Wendland Pdf

This is the second edition of the book which has two additional new chapters on Maxwell’s equations as well as a section on properties of solution spaces of Maxwell’s equations and their trace spaces. These two new chapters, which summarize the most up-to-date results in the literature for the Maxwell’s equations, are sufficient enough to serve as a self-contained introductory book on the modern mathematical theory of boundary integral equations in electromagnetics. The book now contains 12 chapters and is divided into two parts. The first six chapters present modern mathematical theory of boundary integral equations that arise in fundamental problems in continuum mechanics and electromagnetics based on the approach of variational formulations of the equations. The second six chapters present an introduction to basic classical theory of the pseudo-differential operators. The aforementioned corresponding boundary integral operators can now be recast as pseudo-differential operators. These serve as concrete examples that illustrate the basic ideas of how one may apply the theory of pseudo-differential operators and their calculus to obtain additional properties for the corresponding boundary integral operators. These two different approaches are complementary to each other. Both serve as the mathematical foundation of the boundary element methods, which have become extremely popular and efficient computational tools for boundary problems in applications. This book contains a wide spectrum of boundary integral equations arising in fundamental problems in continuum mechanics and electromagnetics. The book is a major scholarly contribution to the modern approaches of boundary integral equations, and should be accessible and useful to a large community of advanced graduate students and researchers in mathematics, physics, and engineering.

Author : Steven G. Krantz
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 53,8 Mb
Release : 2009-05-24
Category : Mathematics
ISBN : 9780817646691

Get Book

Explorations in Harmonic Analysis by Steven G. Krantz Pdf

This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.

Author : Michael E. Taylor
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 48,8 Mb
Release : 2000
Category : Differential equations, Partial
ISBN : 9780821843789

Get Book

Tools for PDE by Michael E. Taylor Pdf

Developing three related tools that are useful in the analysis of partial differential equations (PDEs) arising from the classical study of singular integral operators, this text considers pseudodifferential operators, paradifferential operators, and layer potentials.

Author : Giampiero Esposito
Publisher : Cambridge University Press
Page : 227 pages
File Size : 45,8 Mb
Release : 1998-08-20
Category : Mathematics
ISBN : 9780521648622

Get Book

Dirac Operators and Spectral Geometry by Giampiero Esposito Pdf

A clear, concise and up-to-date introduction to the theory of the Dirac operator and its wide range of applications in theoretical physics for graduate students and researchers.

Author : Hans G. Feichtinger,Bernard Helffer,Michael Lamoureux,Nicolas Lerner,Joachim Toft
Publisher : Springer
Page : 214 pages
File Size : 50,7 Mb
Release : 2008-08-15
Category : Mathematics
ISBN : 9783540682684

Get Book

Pseudo-Differential Operators by Hans G. Feichtinger,Bernard Helffer,Michael Lamoureux,Nicolas Lerner,Joachim Toft Pdf

Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.

Author : Pertti Lounesto
Publisher : Cambridge University Press
Page : 352 pages
File Size : 49,6 Mb
Release : 2001-05-03
Category : Mathematics
ISBN : 9780521005517

Get Book

Clifford Algebras and Spinors by Pertti Lounesto Pdf

This is the second edition of a popular work offering a unique introduction to Clifford algebras and spinors. The beginning chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This edition has three new chapters, including material on conformal invariance and a history of Clifford algebras.

Author : Steve Hofmann
Publisher : American Mathematical Soc.
Page : 91 pages
File Size : 41,5 Mb
Release : 2011
Category : Hardy spaces
ISBN : 9780821852385

Get Book

Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates by Steve Hofmann Pdf

Let $X$ be a metric space with doubling measure, and $L$ be a non-negative, self-adjoint operator satisfying Davies-Gaffney bounds on $L^2(X)$. In this article the authors present a theory of Hardy and BMO spaces associated to $L$, including an atomic (or molecular) decomposition, square function characterization, and duality of Hardy and BMO spaces. Further specializing to the case that $L$ is a Schrodinger operator on $\mathbb{R}^n$ with a non-negative, locally integrable potential, the authors establish additional characterizations of such Hardy spaces in terms of maximal functions. Finally, they define Hardy spaces $H^p_L(X)$ for $p>1$, which may or may not coincide with the space $L^p(X)$, and show that they interpolate with $H^1_L(X)$ spaces by the complex method.

Author : Steve Zelditch
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 50,5 Mb
Release : 2017-12-12
Category : Eigenfunctions
ISBN : 9781470410377

Get Book

Eigenfunctions of the Laplacian on a Riemannian Manifold by Steve Zelditch Pdf

Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.

Author : Friedrich Hirzebruch,Joachim Schwermer,Silke Suter
Publisher : Lecture Notes in Mathematics
Page : 498 pages
File Size : 49,7 Mb
Release : 1985
Category : Mathematics
ISBN : UOM:39015040428321

Get Book

Arbeitstagung Bonn ... by Friedrich Hirzebruch,Joachim Schwermer,Silke Suter Pdf