Download or read book A New Proof of Carleman s Theorem written by Benjamin Epstein and published by . This book was released on 1938 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Carleman s Formulas in Complex Analysis written by L.A. Aizenberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral representations of holomorphic functions play an important part in the classical theory of functions of one complex variable and in multidimensional com plex analysis (in the later case, alongside with integration over the whole boundary aD of a domain D we frequently encounter integration over the Shilov boundary 5 = S(D)). They solve the classical problem of recovering at the points of a do main D a holomorphic function that is sufficiently well-behaved when approaching the boundary aD, from its values on aD or on S. Alongside with this classical problem, it is possible and natural to consider the following one: to recover the holomorphic function in D from its values on some set MeaD not containing S. Of course, M is to be a set of uniqueness for the class of holomorphic functions under consideration (for example, for the functions continuous in D or belonging to the Hardy class HP(D), p ~ 1).
Download or read book Carleman Inequalities written by Nicolas Lerner and published by Springer. This book was released on 2019-05-18 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past 25 years, Carleman estimates have become an essential tool in several areas related to partial differential equations such as control theory, inverse problems, or fluid mechanics. This book provides a detailed exposition of the basic techniques of Carleman Inequalities, driven by applications to various questions of unique continuation. Beginning with an elementary introduction to the topic, including examples accessible to readers without prior knowledge of advanced mathematics, the book's first five chapters contain a thorough exposition of the most classical results, such as Calderón's and Hörmander's theorems. Later chapters explore a selection of results of the last four decades around the themes of continuation for elliptic equations, with the Jerison-Kenig estimates for strong unique continuation, counterexamples to Cauchy uniqueness of Cohen and Alinhac & Baouendi, operators with partially analytic coefficients with intermediate results between Holmgren's and Hörmander's uniqueness theorems, Wolff's modification of Carleman's method, conditional pseudo-convexity, and more. With examples and special cases motivating the general theory, as well as appendices on mathematical background, this monograph provides an accessible, self-contained basic reference on the subject, including a selection of the developments of the past thirty years in unique continuation.
Download or read book Periodic Homogenization of Elliptic Systems written by Zhongwei Shen and published by Springer. This book was released on 2018-09-04 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain. It begins with a review of the classical qualitative homogenization theory, and addresses the problem of convergence rates of solutions. The main body of the monograph investigates various interior and boundary regularity estimates that are uniform in the small parameter e>0. Additional topics include convergence rates for Dirichlet eigenvalues and asymptotic expansions of fundamental solutions, Green functions, and Neumann functions. The monograph is intended for advanced graduate students and researchers in the general areas of analysis and partial differential equations. It provides the reader with a clear and concise exposition of an important and currently active area of quantitative homogenization.
Download or read book Carleman Estimates for Second Order Partial Differential Operators and Applications written by Xiaoyu Fu and published by Springer Nature. This book was released on 2019-10-31 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations, and their typical applications in control, unique continuation, and inverse problems. There are three particularly important and novel features of the book. First, only some basic calculus is needed in order to obtain the main results presented, though some elementary knowledge of functional analysis and partial differential equations will be helpful in understanding them. Second, all Carleman estimates in the book are derived from a fundamental identity for a second order partial differential operator; the only difference is the choice of weight functions. Third, only rather weak smoothness and/or integrability conditions are needed for the coefficients appearing in the equations. Carleman Estimates for Second Order Partial Differential Operators and Applications will be of interest to all researchers in the field.
Download or read book Global Carleman Estimates for Degenerate Parabolic Operators with Applications written by P. Cannarsa and published by American Mathematical Soc.. This book was released on 2016-01-25 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Degenerate parabolic operators have received increasing attention in recent years because they are associated with both important theoretical analysis, such as stochastic diffusion processes, and interesting applications to engineering, physics, biology, and economics. This manuscript has been conceived to introduce the reader to global Carleman estimates for a class of parabolic operators which may degenerate at the boundary of the space domain, in the normal direction to the boundary. Such a kind of degeneracy is relevant to study the invariance of a domain with respect to a given stochastic diffusion flow, and appears naturally in climatology models.
Download or read book Contributions to the Theory of Partial Differential Equations AM 33 Volume 33 written by Lipman Bers and published by Princeton University Press. This book was released on 2016-03-02 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Contributions to the Theory of Partial Differential Equations. (AM-33), Volume 33, will be forthcoming.
Download or read book On Generalizations of Carleman s Theorem and Applications written by Lobna Hammoud Bou Hamdan and published by . This book was released on 2008 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Probability written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-08-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
Download or read book Treatise on the Shift Operator written by N.K. Nikol'skii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an elementary introduction to non-classical spectral theory. Mter the basic definitions and a reduction to the study of the functional model the discussion will be centered around the simplest variant of such a model which, formally speaking, comprises only the class of contraction operators with a one dimensional rank of non-unitarity (rank(I - T*T) = rank(I - TT*) = 1). The main emphasis is on the technical side of the subject, the book being mostly devoted to a development of the analytical machinery of spectral theory rather than to this discipline itself. The functional model of Sz. -Nagy and Foia§ re duces the study of general operators to an investigation of the . compression T=PSIK of the shift operator S, Sf = zf, onto coinvariant subspaces (i. e. subspaces in variant with respect to the adjoint shift S*). In the main body of the book (the "Lectures" in the proper meaning of the word) this operator acts on the Hardy space H2 and is itself a part of the operator of multiplication by the independent variable in the space L2 (in the case at hand L2 means L2(lf), If being the unit circle), this operator again being fundamental for classical spectral theory.
Download or read book Spectral Theory of Differential Operators written by V.A. Il'in and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this fully-illustrated textbook, the author examines the spectral theory of self-adjoint elliptic operators. Chapters focus on the problems of convergence and summability of spectral decompositions about the fundamental functions of elliptic operators of the second order. The author's work offers a novel method for estimation of the remainder term of a spectral function and its Riesz means without recourse to the traditional Carleman technique and Tauberian theorem apparatus.
Download or read book Corrigendum and Improvements to Carleman Estimates Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations and Its Consequences written by Genni Fragnelli and published by American Mathematical Society. This book was released on 2021-11-16 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Proceedings of the London Mathematical Society written by London Mathematical Society and published by . This book was released on 1927 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Papers presented to J. E. Littlewood on his 80th birthday" issued as 3d ser., v. 14 A, 1965.
Download or read book Probability Theory and Mathematical Statistics written by Bronius Grigelionis and published by VSP. This book was released on 1990 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Spectral and Scattering Theory written by Hiroshi Isozaki and published by Springer Nature. This book was released on 2020-09-26 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide basic knowledge of the inverse problems arising in various areas in mathematics, physics, engineering, and medical science. These practical problems boil down to the mathematical question in which one tries to recover the operator (coefficients) or the domain (manifolds) from spectral data. The characteristic properties of the operators in question are often reduced to those of Schrödinger operators. We start from the 1-dimensional theory to observe the main features of inverse spectral problems and then proceed to multi-dimensions. The first milestone is the Borg–Levinson theorem in the inverse Dirichlet problem in a bounded domain elucidating basic motivation of the inverse problem as well as the difference between 1-dimension and multi-dimension. The main theme is the inverse scattering, in which the spectral data is Heisenberg’s S-matrix defined through the observation of the asymptotic behavior at infinity of solutions. Significant progress has been made in the past 30 years by using the Faddeev–Green function or the complex geometrical optics solution by Sylvester and Uhlmann, which made it possible to reconstruct the potential from the S-matrix of one fixed energy. One can also prove the equivalence of the knowledge of S-matrix and that of the Dirichlet-to-Neumann map for boundary value problems in bounded domains. We apply this idea also to the Dirac equation, the Maxwell equation, and discrete Schrödinger operators on perturbed lattices. Our final topic is the boundary control method introduced by Belishev and Kurylev, which is for the moment the only systematic method for the reconstruction of the Riemannian metric from the boundary observation, which we apply to the inverse scattering on non-compact manifolds. We stress that this book focuses on the lucid exposition of these problems and mathematical backgrounds by explaining the basic knowledge of functional analysis and spectral theory, omitting the technical details in order to make the book accessible to graduate students as an introduction to partial differential equations (PDEs) and functional analysis.
Download or read book Generalized harmonic analysis and Tauberian theory classical harmonic and complex analysis written by Norbert Wiener and published by . This book was released on 1976 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Points of Analysis and Their History written by Lars Gårding and published by American Mathematical Soc.. This book was released on 1997 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of small essays containing the history and the proofs of some important and interesting theorems of analysis and partial differential operators in this century. Most of the results in the book are associated with Swedish mathematicians. Also included are the Tarski-Seidenberg theorem and Wiener's classical results in harmonic analysis and a delightful essay on the impact of distributions in analysis. All mathematical points are fully explained, but some require a certain mature understanding from the reader. This book is a well-written, simple work that offers full mathematical treatment, along with insight and fresh points of view. This book is co-published with Higher Education Press (Beijing) and is distributed by the AMS except in China.
