Multilinear Operator Integrals

Author : Anna Skripka,Anna Tomskova
Publisher : Springer Nature
Page : 192 pages
File Size : 42,6 Mb
Release : 2019-12-01
Category : Mathematics
ISBN : 9783030324063

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Multilinear Operator Integrals by Anna Skripka,Anna Tomskova Pdf

This book provides a comprehensive treatment of multilinear operator integral techniques. The exposition is structured to be suitable for a course on methods and applications of multilinear operator integrals and also as a research aid. The ideas and contributions to the field are surveyed and up-to-date results and methods are presented. Most practical constructions of multiple operator integrals are included along with fundamental technical results and major applications to smoothness properties of operator functions (Lipschitz and Hölder continuity, differentiability), approximation of operator functions, spectral shift functions, spectral flow in the setting of noncommutative geometry, quantum differentiability, and differentiability of noncommutative L^p-norms. Main ideas are demonstrated in simpler cases, while more involved, technical proofs are outlined and supplemented with references. Selected open problems in the field are also presented.

Author : Andreas Seeger,Charles K. Smart,Brian Street
Publisher : American Mathematical Soc.
Page : 142 pages
File Size : 55,7 Mb
Release : 2019-02-21
Category : Forms (Mathematics)
ISBN : 9781470434373

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Multilinear Singular Integral Forms of Christ-Journé Type by Andreas Seeger,Charles K. Smart,Brian Street Pdf

Author : Sagun Chanillo,Bruno Franchi,Guozhen Lu,Carlos Perez,Eric T. Sawyer
Publisher : Birkhäuser
Page : 301 pages
File Size : 55,7 Mb
Release : 2017-02-20
Category : Mathematics
ISBN : 9783319527420

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Harmonic Analysis, Partial Differential Equations and Applications by Sagun Chanillo,Bruno Franchi,Guozhen Lu,Carlos Perez,Eric T. Sawyer Pdf

This collection of articles and surveys is devoted to Harmonic Analysis, related Partial Differential Equations and Applications and in particular to the fields of research to which Richard L. Wheeden made profound contributions. The papers deal with Weighted Norm inequalities for classical operators like Singular integrals, fractional integrals and maximal functions that arise in Harmonic Analysis. Other papers deal with applications of Harmonic Analysis to Degenerate Elliptic equations, variational problems, Several Complex variables, Potential theory, free boundaries and boundary behavior of functions.

Author : Yves Meyer,Ronald Coifman
Publisher : Cambridge University Press
Page : 340 pages
File Size : 47,7 Mb
Release : 1997
Category : Mathematics
ISBN : 0521794730

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Wavelets by Yves Meyer,Ronald Coifman Pdf

A classic exposition of the theory of wavelets from two of the subject's leading experts.

Author : David V. Cruz-Uribe,Alberto Fiorenza
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 52,8 Mb
Release : 2013-02-12
Category : Mathematics
ISBN : 9783034805483

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Variable Lebesgue Spaces by David V. Cruz-Uribe,Alberto Fiorenza Pdf

This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.​

Author : Shanzhen Lu
Publisher : World Scientific
Page : 281 pages
File Size : 54,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812770561

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Singular Integrals and Related Topics by Shanzhen Lu Pdf

This book introduces some important progress in the theory of CalderonOCoZygmund singular integrals, oscillatory singular integrals, and LittlewoodOCoPaley theory over the last decade. It includes some important research results by the authors and their cooperators, such as singular integrals with rough kernels on Block spaces and Hardy spaces, the criterion on boundedness of oscillatory singular integrals, and boundedness of the rough Marcinkiewicz integrals. These results have frequently been cited in many published papers."

Author : Camil Muscalu,Wilhelm Schlag
Publisher : Cambridge University Press
Page : 341 pages
File Size : 55,9 Mb
Release : 2013-01-31
Category : Mathematics
ISBN : 9781107031821

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Classical and Multilinear Harmonic Analysis by Camil Muscalu,Wilhelm Schlag Pdf

This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.

Author : Camil Muscalu,Wilhelm Schlag
Publisher : Cambridge University Press
Page : 341 pages
File Size : 50,8 Mb
Release : 2013-01-31
Category : Mathematics
ISBN : 9781139620468

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Classical and Multilinear Harmonic Analysis: Volume 2 by Camil Muscalu,Wilhelm Schlag Pdf

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.

Author : Heinrich G.W. Begehr,R.P. Gilbert,Joji Kajiwara
Publisher : Springer Science & Business Media
Page : 786 pages
File Size : 43,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302698

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Proceedings of the Second ISAAC Congress by Heinrich G.W. Begehr,R.P. Gilbert,Joji Kajiwara Pdf

This book is the Proceedings of the Second ISAAC Congress. ISAAC is the acronym of the International Society for Analysis, its Applications and Computation. The president of ISAAC is Professor Robert P. Gilbert, the second named editor of this book, e-mail: [email protected]. The Congress is world-wide valued so highly that an application for a grant has been selected and this project has been executed with Grant No. 11-56 from *the Commemorative Association for the Japan World Exposition (1970). The finance of the publication of this book is exclusively the said Grant No. 11-56 from *. Thus, a pair of each one copy of two volumes of this book will be sent to all contributors, who registered at the Second ISAAC Congress in Fukuoka, free of charge by the Kluwer Academic Publishers. Analysis is understood here in the broad sense of the word, includ ing differential equations, integral equations, functional analysis, and function theory. It is the purpose of ISAAC to promote analysis, its applications, and its interaction with computation. With this objective, ISAAC organizes international Congresses for the presentation and dis cussion of research on analysis. ISAAC welcomes new members and those interested in joining ISAAC are encouraged to look at the web site http://www .math. udel.edu/ gilbert/isaac/index.html vi and http://www.math.fu-berlin.de/ rd/ ag/isaac/newton/index.html.

Author : Yoshihiro Sawano,Giuseppe Di Fazio,Denny Ivanal Hakim
Publisher : CRC Press
Page : 316 pages
File Size : 41,6 Mb
Release : 2020-09-16
Category : Mathematics
ISBN : 9781000064070

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Morrey Spaces by Yoshihiro Sawano,Giuseppe Di Fazio,Denny Ivanal Hakim Pdf

Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused mainly generalizations and interpolation of Morrey spaces. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

Author : P. R. Halmos,V. S. Sunder
Publisher : Springer Science & Business Media
Page : 147 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642670169

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Bounded Integral Operators on L 2 Spaces by P. R. Halmos,V. S. Sunder Pdf

The subject. The phrase "integral operator" (like some other mathematically informal phrases, such as "effective procedure" and "geometric construction") is sometimes defined and sometimes not. When it is defined, the definition is likely to vary from author to author. While the definition almost always involves an integral, most of its other features can vary quite considerably. Superimposed limiting operations may enter (such as L2 limits in the theory of Fourier transforms and principal values in the theory of singular integrals), IJ' spaces and abstract Banach spaces may intervene, a scalar may be added (as in the theory of the so-called integral operators of the second kind), or, more generally, a multiplication operator may be added (as in the theory of the so-called integral operators of the third kind). The definition used in this book is the most special of all. According to it an integral operator is the natural "continuous" generali zation of the operators induced by matrices, and the only integrals that appear are the familiar Lebesgue-Stieltjes integrals on classical non-pathological mea sure spaces. The category. Some of the flavor of the theory can be perceived in finite dimensional linear algebra. Matrices are sometimes considered to be an un natural and notationally inelegant way of looking at linear transformations. From the point of view of this book that judgement misses something.

Author : Loukas Grafakos
Publisher : Springer
Page : 636 pages
File Size : 47,7 Mb
Release : 2014-11-13
Category : Mathematics
ISBN : 9781493912308

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Modern Fourier Analysis by Loukas Grafakos Pdf

This text is aimed at graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter. This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary.

Author : Carlos Galindo,Alejandro Melle Hernández,Julio José Moyano-Fernández,Wilson A. Zúñiga-Galindo
Publisher : American Mathematical Society
Page : 311 pages
File Size : 41,8 Mb
Release : 2022-05-11
Category : Mathematics
ISBN : 9781470467791

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$p$-Adic Analysis, Arithmetic and Singularities by Carlos Galindo,Alejandro Melle Hernández,Julio José Moyano-Fernández,Wilson A. Zúñiga-Galindo Pdf

This volume contains the proceedings of the 2019 Lluís A. Santaló Summer School on $p$-Adic Analysis, Arithmetic and Singularities, which was held from June 24–28, 2019, at the Universidad Internacional Menéndez Pelayo, Santander, Spain. The main purpose of the book is to present and analyze different incarnations of the local zeta functions and their multiple connections in mathematics and theoretical physics. Local zeta functions are ubiquitous objects in mathematics and theoretical physics. At the mathematical level, local zeta functions contain geometry and arithmetic information about the set of zeros defined by a finite number of polynomials. In terms of applications in theoretical physics, these functions play a central role in the regularization of Feynman amplitudes and Koba-Nielsen-type string amplitudes, among other applications. This volume provides a gentle introduction to a very active area of research that lies at the intersection of number theory, $p$-adic analysis, algebraic geometry, singularity theory, and theoretical physics. Specifically, the book introduces $p$-adic analysis, the theory of Archimedean, $p$-adic, and motivic zeta functions, singularities of plane curves and their Poincaré series, among other similar topics. It also contains original contributions in the aforementioned areas written by renowned specialists. This book is an important reference for students and experts who want to delve quickly into the area of local zeta functions and their many connections in mathematics and theoretical physics.

Author : Stefania A. M. Marcantognini
Publisher : American Mathematical Soc.
Page : 528 pages
File Size : 43,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803042

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Harmonic Analysis and Operator Theory by Stefania A. M. Marcantognini Pdf

The collection covers a broad spectrum of topics, including: wavelet analysis, Haenkel operators, multimeasure theory, the boundary behavior of the Bergman kernel, interpolation theory, and Cotlar's Lemma on almost orthogonality in the context of L[superscript p] spaces and more...

Author : M. S. Agranovich
Publisher : American Mathematical Soc.
Page : 292 pages
File Size : 53,7 Mb
Release : 2002
Category : Mathematics
ISBN : 0821833030

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Partial Differential Equations by M. S. Agranovich Pdf

Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplecticgeometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and general unbounded domains, linear elliptic problems with a parameter for mixed order systems, infinite-dimensional Schrodinger equations, Navier-Stokes equations, and nonlinear Maxwellequations. The book ends on a historical note with a paper about Vishik's seminar as a whole and a list of selected talks given from 1964 through 1989. The book is suitable for graduate students and researchers in pure and applied mathematics and mathematical physics.