Download or read book Eigenfunction Expansions Operator Algebras and Riemannian Symmetric Spaces written by Robert M Kauffman and published by CRC Press. This book was released on 1996-09-25 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Research Note pays particular attention to studying the convergence of the expansion and to the case where D is a family of partial differential operators. All operators in the natural von Neumann algebraassociated with D, and also unbounded operators affiliated with this algebra, are expanded simultaneously in terms of generalized eigenprojections. These are operators which carry a natural space associated with D into its dual. The elements of the range of these eigenprojections are the eigenfunctions, which solve the appropriate eigenvalue equations by duality. The spectral measure is abstractly defined, but its absolute continuity with respect to Hausdorf measure on the joint spectrum is shown to occur when the eigenfunctions are very well-behaved. Uniqueness results are given showing that any two expansions arise from each other by a simple change of variable. A considerable effort has been made to keep the book self-contained for readers with a background in functional analysis including a basic understanding of the theory of von Neumann algebras. More advanced topics in functional analysis, andan introduction to differential geometry and differential operator theory, mostly without proofs, are given in an extensive section on background material.
Download or read book Expansions in Eigenfunctions of Selfadjoint Operators written by I͡Uriĭ Makarovich Berezanskiĭ and published by American Mathematical Soc.. This book was released on 1968 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Eigenfunction Expansions Associated with Second order Differential Equations written by Edward Charles Titchmarsh and published by . This book was released on 1962 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Eigenfunction expansions associated with second order differential written by Edward Charles Titchmarsh and published by . This book was released on 1958 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Eigenfunction Expansions Associated with Second order Differential Equations written by Edward Charles Titchmarsh and published by . This book was released on 1962 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Slow Viscous Flows Qualitative Features And Quantitative Analysis Using Complex Eigenfunction Expansions With Cd rom written by P N Shankar and published by World Scientific. This book was released on 2007-09-28 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book provides a unified and systematic account of internal, external and unsteady slow viscous flows, including the latest advances of the last decade, some of which are due to the author. The book shows how the method of eigenfunctions, in conjunction with least squares, can be used to solve problems of low Reynolds number flows, including three-dimensional internal and unsteady flows, which until recently were considered intractable. Although the methods used are quantitative, much stress is laid on understanding the qualitative nature of these intriguing flows. A secondary purpose of the book is to explain how the complex eigenfunction method can be used to solve problems in science and engineering.Although primarily aimed at graduate students, academics and research engineers in the areas of fluid mechanics and applied mathematics, care has been taken, through the use of numerous diagrams and much discussion, to explain to the non-specialist the qualitative features of these complex flows./a
Download or read book Eigenfunction Expansions and Scattering Theory for Perturbations of delta written by Norman Shenk and published by . This book was released on 1969 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multiparameter Eigenvalue Problems and Expansion Theorems written by Hans Volkmer and published by Springer. This book was released on 2006-11-14 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained treatment of two of the main problems of multiparameter spectral theory: the existence of eigenvalues and the expansion in series of eigenfunctions. The results are first obtained in abstract Hilbert spaces and then applied to integral operators and differential operators. Special attention is paid to various definiteness conditions which can be imposed on multiparameter eigenvalue problems. The reader is not assumed to be familiar with multiparameter spectral theory but should have some knowledge of functional analysis, in particular of Brower's degree of maps.
Download or read book Two dimensional and Three dimensional Linear Elasticity Solutions by Eigenfunction Expansions and the Boundary Integral Equation Method written by Jing Chang (Graduate of Michigan State University) and published by . This book was released on 1978 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Certain Non Harmonic Fourier Expansions as Eigenfunction Expansions of Non Regular Sturm Liouville Systems written by Agnes Ilona Benedek and published by . This book was released on 1974 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Absolute Convergence of Eigenfunction Expansions written by Gerald Walter Hedstrom and published by . This book was released on 1959 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Matched Eigenfunction Expansions for Rheological Flows written by Steven Arman Trogdon and published by . This book was released on 1980 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sturm Liouville Theory written by Werner O. Amrein and published by Springer Science & Business Media. This book was released on 2005-05-19 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm. It aims at giving an overview of the development of Sturm-Liouville theory from its historical roots to present day research. It is the first time that such a comprehensive survey has been made available in compact form. The contributions come from internationally renowned experts and cover a wide range of developments of the theory. The book can therefore serve both as an introduction to Sturm-Liouville theory and as background for ongoing research. The volume is addressed to researchers in related areas, to advanced students and to those interested in the historical development of mathematics. The book will also be of interest to those involved in applications of the theory to diverse areas such as engineering, fluid dynamics and computational spectral analysis.
Download or read book Convergence and Summability of Eigenfunction Expansions Connected with Elliptic Differential Operators written by Gunnar Bergendal and published by . This book was released on 1959 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Eigenfunction Expansions Associated with Second order Differential Equations written by Edward Charles Titchmarsh and published by . This book was released on 1969 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introductory Applied Quantum and Statistical Mechanics written by Peter L. Hagelstein and published by John Wiley & Sons. This book was released on 2004-03-25 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt: * An applied focus for electrical engineers and materials scientists. * Theoretical results supported with real-world systems and applications. * Includes worked examples and self-study questions. * Solutions manual available.
Download or read book III Scattering Theory written by Michael Reed and published by Elsevier. This book was released on 1979-05-29 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself. As such, it is the most effective means, sometimes the only means, to study microscopic nature. To understand the importance of scattering theory, consider the variety of ways in which it arises. First, there are various phenomena in nature (like the blue of the sky) which are the result of scattering. In order to understand the phenomenon (and to identify it as the result of scattering) one must understand the underlying dynamics and its scattering theory. Second, one often wants to use the scattering of waves or particles whose dynamics on knows to determine the structure and position of small or inaccessible objects. For example, in x-ray crystallography (which led to the discovery of DNA), tomography, and the detection of underwater objects by sonar, the underlying dynamics is well understood. What one would like to construct are correspondences that link, via the dynamics, the position, shape, and internal structure of the object to the scattering data. Ideally, the correspondence should be an explicit formula which allows one to reconstruct, at least approximately, the object from the scattering data. The main test of any proposed particle dynamics is whether one can construct for the dynamics a scattering theory that predicts the observed experimental data. Scattering theory was not always so central the physics. Even thought the Coulomb cross section could have been computed by Newton, had he bothered to ask the right question, its calculation is generally attributed to Rutherford more than two hundred years later. Of course, Rutherford's calculation was in connection with the first experiment in nuclear physics.
