Download or read book Distributions and the Boundary Values of Analytic Functions written by E. J. Beltrami and published by Academic Press. This book was released on 2014-05-12 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributions and the Boundary Values of Analytic Functions focuses on the tools and techniques of distribution theory and the distributional boundary behavior of analytic functions and their applications. The publication first offers information on distributions, including spaces of testing functions, distributions of finite order, convolution and regularization, and testing functions of rapid decay and distributions of slow growth. The text then examines Laplace transform, as well as Laplace transforms of distributions with arbitrary support. The manuscript ponders on distributional boundary values of analytic functions, including causal and passive operators, analytic continuation and uniqueness, boundary value theorems and generalized Hilbert transforms, and representation theorems for half-plane holomorphic functions with S' boundary behavior. The publication is a valuable source of data for researchers interested in distributions and the boundary values of analytic functions.
Download or read book Analytic Functions and Distributions in Physics and Engineering written by Bernard W. Roos and published by John Wiley & Sons. This book was released on 1969 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic functions -- Fourier transforms, causality, and dispersion relations -- The Wiener-Hopf technique -- Boundary value problems for sectionally analytic functions -- Distributions -- Applications in neutron transport theory -- Applications in plasma physics -- Appendix A. Paths, contours, and regions in the complex plane -- Appendix B. Order relations.
Download or read book Distributions and Analytic Functions written by Richard D. Carmichael and published by John Wiley & Sons. This book was released on 1989 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Values and Convolution in Ultradistribution Spaces written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Harmonic Analysis and Boundary Value Problems in the Complex Domain written by M.M. Djrbashian and published by Birkhäuser. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: As is well known, the first decades of this century were a period of elaboration of new methods in complex analysis. This elaboration had, in particular, one char acteristic feature, consisting in the interfusion of some concepts and methods of harmonic and complex analyses. That interfusion turned out to have great advan tages and gave rise to a vast number of significant results, of which we want to mention especially the classical results on the theory of Fourier series in L2 ( -7r, 7r) and their continual analog - Plancherel's theorem on the Fourier transform in L2 ( -00, +00). We want to note also two important Wiener and Paley theorems on parametric integral representations of a subclass of entire functions of expo nential type in the Hardy space H2 over a half-plane. Being under the strong influence of these results, the author began in the fifties a series of investigations in the theory of integral representations of analytic and entire functions as well as in the theory of harmonic analysis in the com plex domain. These investigations were based on the remarkable properties of the asymptotics of the entire function (p, J1 > 0), which was introduced into mathematical analysis by Mittag-Leffler for the case J1 = 1. In the process of investigation, the scope of some classical results was essentially enlarged, and the results themselves were evaluated.
Download or read book Mathematical Methods in Physics written by Philippe Blanchard and published by Birkhäuser. This book was released on 2015-04-07 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas. The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories. All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods. The text is divided into three parts: - Part I: A brief introduction to (Schwartz) distribution theory. Elements from the theories of ultra distributions and (Fourier) hyperfunctions are given in addition to some deeper results for Schwartz distributions, thus providing a rather comprehensive introduction to the theory of generalized functions. Basic properties and methods for distributions are developed with applications to constant coefficient ODEs and PDEs. The relation between distributions and holomorphic functions is considered, as well as basic properties of Sobolev spaces. - Part II: Fundamental facts about Hilbert spaces. The basic theory of linear (bounded and unbounded) operators in Hilbert spaces and special classes of linear operators - compact, Hilbert-Schmidt, trace class, and Schrödinger operators, as needed in quantum physics and quantum information theory – are explored. This section also contains a detailed spectral analysis of all major classes of linear operators, including completeness of generalized eigenfunctions, as well as of (completely) positive mappings, in particular quantum operations. - Part III: Direct methods of the calculus of variations and their applications to boundary- and eigenvalue-problems for linear and nonlinear partial differential operators. The authors conclude with a discussion of the Hohenberg-Kohn variational principle. The appendices contain proofs of more general and deeper results, including completions, basic facts about metrizable Hausdorff locally convex topological vector spaces, Baire’s fundamental results and their main consequences, and bilinear functionals. Mathematical Methods in Physics is aimed at a broad community of graduate students in mathematics, mathematical physics, quantum information theory, physics and engineering, as well as researchers in these disciplines. Expanded content and relevant updates will make this new edition a valuable resource for those working in these disciplines.
Download or read book II Fourier Analysis Self Adjointness written by Michael Reed and published by Elsevier. This book was released on 1975-11-05 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume will serve several purposes: to provide an introduction for graduate students not previously acquainted with the material, to serve as a reference for mathematical physicists already working in the field, and to provide an introduction to various advanced topics which are difficult to understand in the literature. Not all the techniques and application are treated in the same depth. In general, we give a very thorough discussion of the mathematical techniques and applications in quatum mechanics, but provide only an introduction to the problems arising in quantum field theory, classical mechanics, and partial differential equations. Finally, some of the material developed in this volume will not find applications until Volume III. For all these reasons, this volume contains a great variety of subject matter. To help the reader select which material is important for him, we have provided a "Reader's Guide" at the end of each chapter.
Download or read book Principles of Advanced Mathematical Physics written by Robert D. Richtmyer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: A first consequence of this difference in texture concerns the attitude we must take toward some (or perhaps most) investigations in "applied mathe matics," at least when the mathematics is applied to physics. Namely, those investigations have to be regarded as pure mathematics and evaluated as such. For example, some of my mathematical colleagues have worked in recent years on the Hartree-Fock approximate method for determining the structures of many-electron atoms and ions. When the method was intro duced, nearly fifty years ago, physicists did the best they could to justify it, using variational principles, intuition, and other techniques within the texture of physical reasoning. By now the method has long since become part of the established structure of physics. The mathematical theorems that can be proved now (mostly for two- and three-electron systems, hence of limited interest for physics), have to be regarded as mathematics. If they are good mathematics (and I believe they are), that is justification enough. If they are not, there is no basis for saying that the work is being done to help the physicists. In that sense, applied mathematics plays no role in today's physics. In today's division of labor, the task of the mathematician is to create mathematics, in whatever area, without being much concerned about how the mathematics is used; that should be decided in the future and by physics.
Download or read book On Quanta Mind and Matter written by Harald Atmanspacher and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: INSTEAD OF A "FESTSCHRIFT" In June 1998 Hans Primas turned 70 years old. Although he himself is not fond of jubilees and although he likes to play the decimal system of numbers down as contingent, this is nevertheless a suitable occasion to reflect on the professional work of one of the rare distinguished contempo rary scientists who attach equal importance to experimental and theoretical and conceptual lines of research. Hans Primas' interests have covered an enormous range: methods and instruments for nuclear magnetic resonance, theoretical chemistry, C* - and W* -algebraic formulations of quantum me chanics, the measurement problem and its various implications, holism and realism in quantum theory, theory reduction, the work and personality of Wolfgang Pauli, as well as Jungian psychology. In many of these fields he provided important and original food for thought, in some cases going far beyond the everyday business in the scien tific world. As is the case with other scientists who are conceptually inno vative, Hans Primas is read more than he is quoted. His influence is due to his writings. Even with the current flood of publications, he still performs the miracle of having scientists eagerly awaiting his next publication.
Download or read book Functional Analysis Surveys and Recent Results written by and published by Elsevier. This book was released on 1977-01-01 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional Analysis: Surveys and Recent Results
Download or read book Generalized Functions written by Ram P. Kanwal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a more cohesive and sharply focused treatment of fundamental concepts and theoretical background material, with particular attention given to better delineating connections to varying applications Exposition driven by additional examples and exercises
Download or read book Boundary Values and Convolution in Ultradistribution Spaces written by Richard D. Carmichael and published by World Scientific Publishing Company. This book was released on 2007 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the construction and characterization of important ultradistribution spaces and studies properties and calculations of ultradistributions such as boundedness and convolution. Integral transforms of ultradistributions are constructed and analyzed. The general theory of the representation of ultradistributions as boundary values of analytic functions is obtained and the recovery of the analytic functions as Cauchy, Fourier-Laplace, and Poisson integrals associated with the boundary value is proved.Ultradistributions are useful in applications in quantum field theory, partial differential equations, convolution equations, harmonic analysis, pseudo-differential theory, time-frequency analysis, and other areas of analysis. Thus this book is of interest to users of ultradistributions in applications as well as to research mathematicians in areas of analysis.
Download or read book OAR Cumulative Index of Research Results written by and published by . This book was released on 1967 with total page 1264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Prehistory of the Theory of Distributions written by J. Lützen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: I first learned the theory of distributions from Professor Ebbe Thue Poulsen in an undergraduate course at Aarhus University. Both his lectures and the textbook, Topological Vector Spaces, Distributions and Kernels by F. Treves, used in the course, opened my eyes to the beauty and abstract simplicity of the theory. However my incomplete study of many branches of classical analysis left me with the question: Why is the theory of distributions important? In my continued studies this question was gradually answered, but my growing interest in the history of mathematics caused me to alter my question to other questions such as: For what purpose, if any, was the theory of distributions originally created? Who invented distributions and when? I quickly found answers to the last two questions: distributions were invented by S. Sobolev and L. Schwartz around 1936 and 1950, respectively. Knowing this answer, however, only created a new question: Did Sobolev and Schwartz construct distributions from scratch or were there earlier trends and, if so, what were they? It is this question, concerning the pre history of the theory of distributions, which I attempt to answer in this book. Most of my research took place at the History of Science Department of Aarhus University. I wish to thank this department for its financial and intellectual support. I am especially grateful to Lektors Kirsti Andersen from the History of Science Department and Lars Mejlbo from the Mathematics Department, for their kindness, constructive criticism, and encouragement.
Download or read book Non Homogeneous Boundary Value Problems and Applications written by Jacques Louis Lions and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Our essential objective is the study of the linear, non-homogeneous problems: (1) Pu = I in CD, an open set in RN, (2) fQjtl = gj on am (boundary of m), lor on a subset of the boundm"J am 1
Download or read book Generalized Analytic Functions written by Ilʹi︠a︡ Nestorovich Vekua and published by Pergamon. This book was released on 1962 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lumped and Distributed Passive Networks written by M. Ronald Wohlers and published by Academic Press. This book was released on 2013-10-22 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lumped and Distributed Passive Networks: A Generalized and Advanced Viewpoint considers the mathematical study of a subset of passive linear operators. This five-chapter focuses on the questions of analysis and representation of such operators and illustrates the results of these analyses by obtaining some of the limitations that are imposed on the performance of passive systems. The first two chapters deal with the structure of general linear passive operators. These chapters specifically look into the theory of distributions, called generalized functions. The third and fourth chapters illustrate the application of passive operator theory to rational (lumped) and irrational (distributed) systems. The fifth chapter discusses some applications of optimization theory to the study of networks.
