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Author: Elias M. Stein
Publisher: Princeton University Press
ISBN: 1400883881
Category : Mathematics
Languages : en
Pages : 304
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Book Description
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.
Author: Elias M. Stein
Publisher: Princeton University Press
ISBN: 1400883881
Category : Mathematics
Languages : en
Pages : 304
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Book Description
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.
Author: N. I. Muskhelishvili
Publisher: Courier Corporation
ISBN: 0486145069
Category : Mathematics
Languages : en
Pages : 466
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Book Description
DIVHigh-level treatment of one-dimensional singular integral equations covers Holder Condition, Hilbert and Riemann-Hilbert problems, Dirichlet problem, more. 1953 edition. /div
Author: Guy David
Publisher: Springer
ISBN: 3540463771
Category : Mathematics
Languages : en
Pages : 119
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Book Description
Wavelets are a recently developed tool for the analysis and synthesis of functions; their simplicity, versatility and precision makes them valuable in many branches of applied mathematics. The book begins with an introduction to the theory of wavelets and limits itself to the detailed construction of various orthonormal bases of wavelets. A second part centers on a criterion for the L2-boundedness of singular integral operators: the T(b)-theorem. It contains a full proof of that theorem. It contains a full proof of that theorem, and a few of the most striking applications (mostly to the Cauchy integral). The third part is a survey of recent attempts to understand the geometry of subsets of Rn on which analogues of the Cauchy kernel define bounded operators. The book was conceived for a graduate student, or researcher, with a primary interest in analysis (and preferably some knowledge of harmonic analysis and seeking an understanding of some of the new "real-variable methods" used in harmonic analysis.
Author: Frédéric Pham
Publisher: Springer Science & Business Media
ISBN: 0857296035
Category : Mathematics
Languages : en
Pages : 218
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Book Description
Bringing together two fundamental texts from Frédéric Pham’s research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Using notions developed by J. Leray in the calculus of residues in several variables and R. Thom’s isotopy theorems, Frédéric Pham’s foundational study of the singularities of integrals lies at the interface between analysis and algebraic geometry, culminating in the Picard-Lefschetz formulae. These mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from the point of view of hyperfunction theory and microlocal analysis. Providing a ‘must-have’ introduction to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. This book will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frédéric Pham, now retired, was Professor at the University of Nice. He has published several educational and research texts. His recent work concerns semi-classical analysis and resurgent functions.
Author: S. G. Mikhlin
Publisher: Elsevier
ISBN: 1483164497
Category : Mathematics
Languages : en
Pages : 273
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Book Description
Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.
Author: Shanzhen Lu
Publisher: World Scientific
ISBN: 9812770569
Category : Mathematics
Languages : en
Pages : 281
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Book Description
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: Ricardo Estrada
Publisher: Springer Science & Business Media
ISBN: 1461213827
Category : Mathematics
Languages : en
Pages : 433
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Book Description
Many physical problems that are usually solved by differential equation techniques can be solved more effectively by integral equation methods. This work focuses exclusively on singular integral equations and on the distributional solutions of these equations. A large number of beautiful mathematical concepts are required to find such solutions, which in tum, can be applied to a wide variety of scientific fields - potential theory, me chanics, fluid dynamics, scattering of acoustic, electromagnetic and earth quake waves, statistics, and population dynamics, to cite just several. An integral equation is said to be singular if the kernel is singular within the range of integration, or if one or both limits of integration are infinite. The singular integral equations that we have studied extensively in this book are of the following type. In these equations f (x) is a given function and g(y) is the unknown function. 1. The Abel equation x x) = l g (y) d 0
Author: Solomon G. Mikhlin
Publisher: Springer Science & Business Media
ISBN: 9783540159674
Category : Mathematics
Languages : en
Pages : 530
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Book Description
The present edition differs from the original German one mainly in the following addi tional material: weighted norm inequalities for maximal functions and singular opera tors (§ 12, Chap. XI), polysingular integral operators and pseudo-differential operators (§§ 7, 8, Chap. XII), and spline approximation methods for solving singular integral equations (§ 4, Chap. XVII). Furthermore, we added two subsections on polynomial approximation methods for singular integral equations over an interval or with dis continuous coefficients (Nos. 3.6 and 3.7, Chap. XVII). In many places we incorporated new results which, in the vast majority, are from the last five years after publishing the German edition (note that the references are enlarged by about 150 new titles). S. G. Mikhlin wrote §§ 7, 8, Chap. XII, and the other additions were drawn up by S. Prossdorf. We wish to express our deepest gratitude to Dr. A. Bottcher and Dr. R. Lehmann who together translated the text into English carefully and with remarkable expertise.
Author: Prof. Kevin F. Clancey
Publisher: Birkhäuser
ISBN: 3034854927
Category : Science
Languages : en
Pages : 246
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Book Description
A few years aga the authors started a project of a book on the theory of systems of one-dimensional singular integral equa tions which was planned as a continuation of the monograph by one of the authors and N. Ya. Krupnik ~~ concerning scalar equa tions. This set of notes was initiated as a chapter dealing with problems of factorization of matrix functions vis-a-vis appli cations to systems of singular integral equations. Working systematically onthischapter and adding along the way new points of view, new proofs and results, we finally saw that the material connected with factorizations is of independent interest and we decided to publish this chapter as aseparate volume. In fact, because of recent activity, the amount of material was quite large and we quickly learned that we cannot cover all of the results in complete detail. We have tried to include a represen tative variety of all kinds of methods, techniques,results and applications. Apart of the current work exposes results from the Russian literature which have never appeared in English translation. We have also decided to reflect some of the recent results which make interesting connections between factorization of matrix functions and systems theory. The field remains very active and many results and connec tions are still not weIl understood. These notes should be viewed as a stepping stone to further development. The authors hope that sometime they will return to complete their original plan.
Author: Umberto Neri
Publisher: Springer
ISBN: 3540368647
Category : Mathematics
Languages : en
Pages : 279
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Book Description
