Harmonic Analysis (PMS-43)

Real-Variable Methods, Orthogonality, and Oscillatory Integrals. (PMS-43)

Author: Elias M. Stein

Publisher: Princeton University Press

ISBN: 140088392X

Category: Mathematics

Page: 712

View: 7443

This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, L\sup\ estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.

Harmonic Analysis

Real-variable Methods, Orthogonality, and Oscillatory Integrals

Author: Elias M. Stein,Timothy S. Murphy

Publisher: Princeton University Press

ISBN: 9780691032160

Category: Mathematics

Page: 695

View: 9401

This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, L\sup\ estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.

Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)

Author: Elias M. Stein

Publisher: Princeton University Press

ISBN: 1400881870

Category: Mathematics

Page: 160

View: 6741

This work deals with an extension of the classical Littlewood-Paley theory in the context of symmetric diffusion semigroups. In this general setting there are applications to a variety of problems, such as those arising in the study of the expansions coming from second order elliptic operators. A review of background material in Lie groups and martingale theory is included to make the monograph more accessible to the student.

Classical and Multilinear Harmonic Analysis

Author: Camil Muscalu,Wilhelm Schlag

Publisher: Cambridge University Press

ISBN: 0521882451

Category: Mathematics

Page: 387

View: 1003

"This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained, and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderâon-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; Calderâon's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form"--

Complex Analysis

Author: Elias M. Stein,Rami Shakarchi

Publisher: Princeton University Press

ISBN: 1400831156

Category: Mathematics

Page: 400

View: 983

With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Fourier Analysis

Author: Javier Duoandikoetxea Zuazo

Publisher: American Mathematical Soc.

ISBN: 9780821883846

Category: Mathematics

Page: 222

View: 8129

Bliss

Author: Kathryn Littlewood

Publisher: Harper Collins

ISBN: 0062084259

Category: Juvenile Fiction

Page: 400

View: 1321

The perfect novel for young readers who love baking and magic! Rosemary Bliss's family has a secret. It's the Bliss Cookery Booke—an ancient, leather-bound volume of enchanted recipes like Singing Gingersnaps. Rose and her siblings are supposed to keep the Cookery Booke locked away while their parents are out of town, but then a mysterious stranger shows up. "Aunt" Lily rides a motorcycle and also whips up exotic (but delicious) dishes for dinner. Soon boring, non-magical recipes feel like life before Aunt Lily—a lot less fun. So Rose and her siblings experiment with just a couple of recipes from the forbidden Cookery Booke. A few Love Muffins and Cookies of Truth couldn't cause too much trouble . . . could they? Kathryn Littlewood's culinary caper blends rich emotional flavor with truly enchanting wit, yielding one heaping portion of hilarious family adventure.

Essays on Fourier Analysis in Honor of Elias M. Stein (PMS-42)

Author: Charles Fefferman,Robert Fefferman,Stephen Wainger

Publisher: Princeton University Press

ISBN: 1400852943

Category: Mathematics

Page: 396

View: 7504

This book contains the lectures presented at a conference held at Princeton University in May 1991 in honor of Elias M. Stein's sixtieth birthday. The lectures deal with Fourier analysis and its applications. The contributors to the volume are W. Beckner, A. Boggess, J. Bourgain, A. Carbery, M. Christ, R. R. Coifman, S. Dobyinsky, C. Fefferman, R. Fefferman, Y. Han, D. Jerison, P. W. Jones, C. Kenig, Y. Meyer, A. Nagel, D. H. Phong, J. Vance, S. Wainger, D. Watson, G. Weiss, V. Wickerhauser, and T. H. Wolff. The topics of the lectures are: conformally invariant inequalities, oscillatory integrals, analytic hypoellipticity, wavelets, the work of E. M. Stein, elliptic non-smooth PDE, nodal sets of eigenfunctions, removable sets for Sobolev spaces in the plane, nonlinear dispersive equations, bilinear operators and renormalization, holomorphic functions on wedges, singular Radon and related transforms, Hilbert transforms and maximal functions on curves, Besov and related function spaces on spaces of homogeneous type, and counterexamples with harmonic gradients in Euclidean space. Originally published in 1995. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Singular Integrals and Differentiability Properties of Functions (PMS-30)

Author: Elias M. Stein

Publisher: Princeton University Press

ISBN: 1400883881

Category: Mathematics

Page: 304

View: 6733

Singular integrals are among the most interesting and important objects of study in analysis, one of the three main branches of mathematics. They deal with real and complex numbers and their functions. In this book, Princeton professor Elias Stein, a leading mathematical innovator as well as a gifted expositor, produced what has been called the most influential mathematics text in the last thirty-five years. One reason for its success as a text is its almost legendary presentation: Stein takes arcane material, previously understood only by specialists, and makes it accessible even to beginning graduate students. Readers have reflected that when you read this book, not only do you see that the greats of the past have done exciting work, but you also feel inspired that you can master the subject and contribute to it yourself. Singular integrals were known to only a few specialists when Stein's book was first published. Over time, however, the book has inspired a whole generation of researchers to apply its methods to a broad range of problems in many disciplines, including engineering, biology, and finance. Stein has received numerous awards for his research, including the Wolf Prize of Israel, the Steele Prize, and the National Medal of Science. He has published eight books with Princeton, including Real Analysis in 2005.

Harmonic Analysis

Real-variable Methods, Orthogonality, and Oscillatory Integrals

Author: Elias M. Stein,Timothy S. Murphy

Publisher: N.A

ISBN: 9780691032160

Category: Mathematics

Page: 695

View: 2005

This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, L\sup\ estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.

Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48)

Author: Kari Astala,Tadeusz Iwaniec,Gaven Martin

Publisher: Princeton University Press

ISBN: 9780691137773

Category: Mathematics

Page: 677

View: 7946

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.

Shape in Picture

Mathematical Description of Shape in Grey-level Images

Author: O Ying Lie,Alexander Toet,David Foster,Henk J.A.M. Heijmans,Peter Meer

Publisher: Springer Science & Business Media

ISBN: 366203039X

Category: Computers

Page: 682

View: 1074

The fields of image analysis, computer vision, and artificial intelligence all make use of descriptions of shape in grey-level images. Most existing algorithms for the automatic recognition and classification of particular shapes have been devel oped for specific purposes, with the result that these methods are often restricted in their application. The use of advanced and theoretically well-founded math ematical methods should lead to the construction of robust shape descriptors having more general application. Shape description can be regarded as a meeting point of vision research, mathematics, computing science, and the application fields of image analy sis, computer vision, and artificial intelligence. The NATO Advanced Research Workshop "Shape in Picture" was organised with a twofold objective: first, it should provide all participants with an overview of relevant developments in these different disciplines; second, it should stimulate researchers to exchange original results and ideas across the boundaries of these disciplines. This book comprises a widely drawn selection of papers presented at the workshop, and many contributions have been revised to reflect further progress in the field. The focus of this collection is on mathematical approaches to the construction of shape descriptions from grey-level images. The book is divided into five parts, each devoted to a different discipline. Each part contains papers that have tutorial sections; these are intended to assist the reader in becoming acquainted with the variety of approaches to the problem.

A Primer on Mapping Class Groups (PMS-49)

Author: Benson Farb,Dan Margalit

Publisher: Princeton University Press

ISBN: 1400839041

Category: Mathematics

Page: 512

View: 5984

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

Theory of Lie Groups (PMS-8)

Author: Claude Chevalley

Publisher: Princeton University Press

ISBN: 1400883857

Category: Mathematics

Page: 232

View: 8112

This famous book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this idea to its fullest extent, Chevalley incorporated a broad range of topics, such as the covering spaces of topological spaces, analytic manifolds, integration of complete systems of differential equations on a manifold, and the calculus of exterior differential forms. The book opens with a short description of the classical groups: unitary groups, orthogonal groups, symplectic groups, etc. These special groups are then used to illustrate the general properties of Lie groups, which are considered later. The general notion of a Lie group is defined and correlated with the algebraic notion of a Lie algebra; the subgroups, factor groups, and homomorphisms of Lie groups are studied by making use of the Lie algebra. The last chapter is concerned with the theory of compact groups, culminating in Peter-Weyl's theorem on the existence of representations. Given a compact group, it is shown how one can construct algebraically the corresponding Lie group with complex parameters which appears in the form of a certain algebraic variety (associated algebraic group). This construction is intimately related to the proof of the generalization given by Tannaka of Pontrjagin's duality theorem for Abelian groups. The continued importance of Lie groups in mathematics and theoretical physics make this an indispensable volume for researchers in both fields.

Character Recognition Systems

A Guide for Students and Practitioners

Author: Mohamed Cheriet,Nawwaf Kharma,Cheng-Lin Liu,Ching Suen

Publisher: John Wiley & Sons

ISBN: 9780470176528

Category: Technology & Engineering

Page: 351

View: 9361

"Much of pattern recognition theory and practice, including methods such as Support Vector Machines, has emerged in an attempt to solve the character recognition problem. This book is written by very well-known academics who have worked in the field for many years and have made significant and lasting contributions. The book will no doubt be of value to students and practitioners." -Sargur N. Srihari, SUNY Distinguished Professor, Department of Computer Science and Engineering, and Director, Center of Excellence for Document Analysis and Recognition (CEDAR), University at Buffalo, The State University of New York "The disciplines of optical character recognition and document image analysis have a history of more than forty years. In the last decade, the importance and popularity of these areas have grown enormously. Surprisingly, however, the field is not well covered by any textbook. This book has been written by prominent leaders in the field. It includes all important topics in optical character recognition and document analysis, and is written in a very coherent and comprehensive style. This book satisfies an urgent need. It is a volume the community has been awaiting for a long time, and I can enthusiastically recommend it to everybody working in the area." -Horst Bunke, Professor, Institute of Computer Science and Applied Mathematics (IAM), University of Bern, Switzerland In Character Recognition Systems, the authors provide practitioners and students with the fundamental principles and state-of-the-art computational methods of reading printed texts and handwritten materials. The information presented is analogous to the stages of a computer recognition system, helping readers master the theory and latest methodologies used in character recognition in a meaningful way. This book covers: * Perspectives on the history, applications, and evolution of Optical Character Recognition (OCR) * The most widely used pre-processing techniques, as well as methods for extracting character contours and skeletons * Evaluating extracted features, both structural and statistical * Modern classification methods that are successful in character recognition, including statistical methods, Artificial Neural Networks (ANN), Support Vector Machines (SVM), structural methods, and multi-classifier methods * An overview of word and string recognition methods and techniques * Case studies that illustrate practical applications, with descriptions of the methods and theories behind the experimental results Each chapter contains major steps and tricks to handle the tasks described at-hand. Researchers and graduate students in computer science and engineering will find this book useful for designing a concrete system in OCR technology, while practitioners will rely on it as a valuable resource for the latest advances and modern technologies that aren't covered elsewhere in a single book.

Synchronization

From Simple to Complex

Author: Alexander Balanov,Natalia Janson,Dmitry Postnov,Olga Sosnovtseva

Publisher: Springer Science & Business Media

ISBN: 3540721282

Category: Science

Page: 426

View: 5836

This fascinating work is devoted to the fundamental phenomenon in physics – synchronization that occurs in coupled non-linear dissipative oscillators. Examples of such systems range from mechanical clocks to population dynamics, from the human heart to neural networks. The main purpose of this book is to demonstrate that the complexity of synchronous patterns of real oscillating systems can be described in the framework of the general approach, and the authors study this phenomenon as applied to oscillations of different types, such as those with periodic, chaotic, noisy and noise-induced nature.

Residual Stress and Stress Relaxation

Author: Eric Kula

Publisher: Springer Science & Business Media

ISBN: 1489918841

Category: Science

Page: 535

View: 8911

The Army Materials and Mechanics Research Center in coop eration with the Materials Science Group of the Department of Chemical Engineering and Materials Science of Syracuse University has been conducting the Annual Sagamore Army Materials Research Conference since 1954. The specific purpose of these conferences has been to bring together scientists and engineers from academic institutions, industry and government who are uniquely qualified to explore in depth a subject of importance to the Department of Defense, the Army and the scientific community. These proceedings, entitled RESIDUAL STRESS AND STRESS RELAXATION, address the nature of residual stresses and their measurements, the sources of residual stress, stress relaxation, sub-critical crack growth in the presence of residual stress, residual stresses and properties, and research in progress. We wish to acknowledge the assistance of Mr. Dan McNaught of the Army Materials and Mechanics Research Center and Mr. Robert J. Sell and Helen Brown DeMascio of Syracuse University throughout the stages of the conference planning and finally the publication of the book. The continued active interest and support of these conferences by Dr. E. Wright, Director of the Army Materials and Mechanics Research Center, is appreciated.

Motives, Quantum Field Theory, and Pseudodifferential Operators

Conference on Motives, Quantum Field Theory, and Pseudodifferential Operators, June 2-13, 2008, Boston University, Boston, Massachusetts

Author: Alan L. Carey

Publisher: American Mathematical Soc.

ISBN: 0821851993

Category: Mathematics

Page: 349

View: 5125

This volume contains articles related to the conference ``Motives, Quantum Field Theory, and Pseudodifferntial Operators'' held at Boston University in June 2008, with partial support from the Clay Mathematics Institute, Boston University, and the National Science Foundation. There are deep but only partially understood connections between the three conference fields, so this book is intended both to explain the known connections and to offer directions for further research. In keeping with the organization of the conference, this book contains introductory lectures on each of the conference themes and research articles on current topics in these fields. The introductory lectures are suitable for graduate students and new Ph.D.'s in both mathematics and theoretical physics, as well as for senior researchers, since few mathematicians are expert in any two of the conference areas. Among the topics discussed in the introductory lectures are the appearance of multiple zeta values both as periods of motives and in Feynman integral calculations in perturbative QFT, the use of Hopf algebra techniques for renormalization in QFT, and regularized traces of pseudodifferential operators. The motivic interpretation of multiple zeta values points to a fundamental link between motives and QFT, and there are strong parallels between regularized traces and Feynman integral techniques. The research articles cover a range of topics in areas related to the conference themes, including geometric, Hopf algebraic, analytic, motivic and computational aspects of quantum field theory and mirror symmetry. There is no unifying theory of the conference areas at present, so the research articles present the current state of the art pointing towards such a unification.

Cybernetics Oriented Programming (CYBOP)

An Investigation on the Applicability of Inter-disciplinary Concepts to Software System Development

Author: Christian Heller

Publisher: CYBOP

ISBN: 3981089804

Category: Computer software

Page: 512

View: 5314