Download or read book The logarithmic potential in higher dimensions written by Bent Fuglede and published by . This book was released on 1960 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Logarithmic Potential in Higher Dimensions written by Bent Fuglede and published by . This book was released on 1960 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Schwarz Function and Its Generalization to Higher Dimensions written by Harold S. Shapiro and published by John Wiley & Sons. This book was released on 1992-04-16 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Schwarz function originates in classical complex analysis and potential theory. Here the author presents the advantages favoring a mode of treatment which unites the subject with modern theory of distributions and partial differential equations thus bridging the gap between two-dimensional geometric and multi-dimensional analysts. Examines the Schwarz function and its relationship to recent investigations regarding inverse problems of Newtonian gravitation, free boundaries, Hele-Shaw flows and the propagation of singularities for holomorphic p.d.e.
Download or read book Logarithmic Potentials with External Fields written by Edward B. Saff and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years approximation theory and the theory of orthogonal polynomials have witnessed a dramatic increase in the number of solutions of difficult and previously untouchable problems. This is due to the interaction of approximation theoretical techniques with classical potential theory (more precisely, the theory of logarithmic potentials, which is directly related to polynomials and to problems in the plane or on the real line). Most of the applications are based on an exten sion of classical logarithmic potential theory to the case when there is a weight (external field) present. The list of recent developments is quite impressive and includes: creation of the theory of non-classical orthogonal polynomials with re spect to exponential weights; the theory of orthogonal polynomials with respect to general measures with compact support; the theory of incomplete polynomials and their widespread generalizations, and the theory of multipoint Pade approximation. The new approach has produced long sought solutions for many problems; most notably, the Freud problems on the asymptotics of orthogonal polynomials with a respect to weights of the form exp(-Ixl ); the "l/9-th" conjecture on rational approximation of exp(x); and the problem of the exact asymptotic constant in the rational approximation of Ixl. One aim of the present book is to provide a self-contained introduction to the aforementioned "weighted" potential theory as well as to its numerous applications. As a side-product we shall also fully develop the classical theory of logarithmic potentials.
Download or read book Wave Equations in Higher Dimensions written by Shi-Hai Dong and published by Springer Science & Business Media. This book was released on 2011-07-09 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativistic and relativistic quantum mechanics in terms of the theories presented in Part II. In particular, the Levinson theorem and the generalized hypervirial theorem in higher dimensions, the Schrödinger equation with position-dependent mass and the Kaluza-Klein theory in higher dimensions are investigated. In this context, the dependence of the energy levels on the dimension is shown. Finally, Part V contains conclusions, outlooks and an extensive bibliography.
Download or read book High Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Download or read book Foundations of Potential Theory written by Oliver Dimon Kellogg and published by Courier Corporation. This book was released on 1953-01-01 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to fundamentals of potential functions covers the force of gravity, fields of force, potentials, harmonic functions, electric images and Green's function, sequences of harmonic functions, fundamental existence theorems, the logarithmic potential, and much more. Detailed proofs rigorously worked out. 1929 edition.
Download or read book The Logarithmic Potential written by Griffith Conrad Evans and published by . This book was released on 1927 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies fundamental properties of the logarithmic potential and their connections to the theory of Fourier series, to potential theory, and to function theory. The material centers around a study of Poisson's integral in two dimensions and of the corresponding Stieltjes integral. The results are then extended to the integrals in terms of Green's functions for general regions. There are some thirty exercises scattered throughout the text. These are designed in part to familiarize the reader with the concepts introduced, and in part to complement the theory. The reader should know something of potential theory, functions of a complex variable, and Lebesgue integrals. The book is based on lectures given by the author in 1924-1925 at the Rice Institute and at the University of Chicago.
Download or read book High Dimensional Covariance Estimation written by Mohsen Pourahmadi and published by John Wiley & Sons. This book was released on 2013-05-28 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.
Download or read book Classical and Multilinear Harmonic Analysis Volume 1 written by Camil Muscalu and published by Cambridge University Press. This book was released on 2013-01-31 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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.
Download or read book Analysis and Partial Differential Equations on Manifolds Fractals and Graphs written by Alexander Grigor'yan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-01-18 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.
Download or read book Recent Developments in Several Complex Variables AM 100 Volume 100 written by John Erik Fornaess and published by Princeton University Press. This book was released on 2016-03-02 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Recent Developments in Several Complex Variables. (AM-100), Volume 100, will be forthcoming.
Download or read book An Introduction to Partial Differential Equations with MATLAB written by Matthew P. Coleman and published by CRC Press. This book was released on 2016-04-19 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Partial Differential Equations with MATLAB, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat,
Download or read book Foundations of Potential Theory written by Oliver Dimon Kellogg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume gives a systematic treatment of potential functions. It takes its origin in two courses, one elementary and one advanced, which the author has given at intervals during the last ten years, and has a two-fold purpose: first, to serve as an introduction for students whose attainments in the Calculus include some knowledge of partial derivatives and multiple and line integrals; and secondly, to provide the reader with the fundamentals of the subject, so that he may proceed immediately to the applications, or to the periodical literature of the day. It is inherent in the nature of the subject that physical intuition and illustration be appealed to freely, and this has been done. However, that the book may present sound ideals to the student, and in order also serve the mathematician, both for purposes of reference and as a basis for further developments, the proofs have been given by rigorous methods. This has led, at a number of points, to results either not found elsewhere, or not readily accessible. Thus, Chapter IV contains a proof for the general regular region of the divergence theorem (Gauss', or Green's theorem) on the reduction of volume to surface integrals. The treatment of the fundamental existence theorems in Chapter XI by means of integral equations meets squarely the difficulties incident to ·the discontinuity of the kernel, and the same chapter gives an account of the most recent developments with respect to the Dirichlet problem.
Download or read book Fourier Analysis written by Javier Duoandikoetxea Zuazo and published by American Mathematical Soc.. This book was released on 2001 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies the real variable methods introduced into Fourier analysis by A. P. Calderon and A. Zygmund in the 1950s. Contains chapters on Fourier series and integrals, the Hardy-Littlewood maximal function, the Hilbert transform, singular integrals, H1 and BMO, weighted inequalities, Littlewood-Paley theory and multipliers, and the T1 theorem. Published in Spanish by Addison-Wesley and Universidad Autonoma de Madrid in 1995. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Fourier Analysis written by Javier Duoandikoetxea and published by American Mathematical Society. This book was released on 2024-04-04 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier analysis encompasses a variety of perspectives and techniques. This volume presents the real variable methods of Fourier analysis introduced by Calderón and Zygmund. The text was born from a graduate course taught at the Universidad Autónoma de Madrid and incorporates lecture notes from a course taught by José Luis Rubio de Francia at the same university. Motivated by the study of Fourier series and integrals, classical topics are introduced, such as the Hardy-Littlewood maximal function and the Hilbert transform. The remaining portions of the text are devoted to the study of singular integral operators and multipliers. Both classical aspects of the theory and more recent developments, such as weighted inequalities, $H^1$, $BMO$ spaces, and the $T1$ theorem, are discussed. Chapter 1 presents a review of Fourier series and integrals; Chapters 2 and 3 introduce two operators that are basic to the field: the Hardy-Littlewood maximal function and the Hilbert transform. Chapters 4 and 5 discuss singular integrals, including modern generalizations. Chapter 6 studies the relationship between $H^1$, $BMO$, and singular integrals; Chapter 7 presents the elementary theory of weighted norm inequalities. Chapter 8 discusses Littlewood-Paley theory, which had developments that resulted in a number of applications. The final chapter concludes with an important result, the $T1$ theorem, which has been of crucial importance in the field. This volume has been updated and translated from the Spanish edition that was published in 1995. Minor changes have been made to the core of the book; however, the sections, “Notes and Further Results” have been considerably expanded and incorporate new topics, results, and references. It is geared toward graduate students seeking a concise introduction to the main aspects of the classical theory of singular operators and multipliers. Prerequisites include basic knowledge in Lebesgue integrals and functional analysis.
Download or read book Integral Operators in Potential Theory written by Josef Kral and published by Springer. This book was released on 2006-11-15 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt:
