Spectral Analysis Of Differential Operators
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| Author | : Fedor S. Rofe-Beketov |
| Publisher | : World Scientific |
| Total Pages | : 463 |
| Release | : 2005 |
| Genre | : Science |
| ISBN | : 9812562761 |
Download Spectral Analysis of Differential Operators Book in PDF, Epub and Kindle
- Detailed bibliographical comments and some open questions are given after each chapter - Indicates connections between the content of the book and many other topics in mathematics and physics - Open questions are formulated and commented with the intention to attract attention of young mathematicians
| Author | : Joachim Weidmann |
| Publisher | : Springer |
| Total Pages | : 310 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540479120 |
Download Spectral Theory of Ordinary Differential Operators Book in PDF, Epub and Kindle
These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating on -valued functions existence and construction of self-adjoint realizations via boundary conditions, determination and study of general properties of the resolvent, spectral representation and spectral resolution. Special attention is paid to the question of separated boundary conditions, spectral multiplicity and absolutely continuous spectrum. For the case nm=2 (Sturm-Liouville operators and Dirac systems) the classical theory of Weyl-Titchmarch is included. Oscillation theory for Sturm-Liouville operators and Dirac systems is developed and applied to the study of the essential and absolutely continuous spectrum. The results are illustrated by the explicit solution of a number of particular problems including the spectral theory one partical Schrödinger and Dirac operators with spherically symmetric potentials. The methods of proof are functionally analytic wherever possible.
| Author | : D. E. Edmunds |
| Publisher | : Springer |
| Total Pages | : 322 |
| Release | : 2018-11-20 |
| Genre | : Mathematics |
| ISBN | : 3030021254 |
Download Elliptic Differential Operators and Spectral Analysis Book in PDF, Epub and Kindle
This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature. Starting with the basics of elliptic operators and their naturally associated function spaces, the authors then proceed to cover various related topics of current and continuing importance. Particular attention is given to the characterisation of self-adjoint extensions of symmetric operators acting in a Hilbert space and, for elliptic operators, the realisation of such extensions in terms of boundary conditions. A good deal of material not previously available in book form, such as the treatment of the Schauder estimates, is included. Requiring only basic knowledge of measure theory and functional analysis, the book is accessible to graduate students and will be of interest to all researchers in partial differential equations. The reader will value its self-contained, thorough and unified presentation of the modern theory of elliptic operators.
| Author | : M.A. Shubin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 278 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662067196 |
Download Partial Differential Equations VII Book in PDF, Epub and Kindle
This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. Also including a special section of Sunada's recent solution of Kac's celebrated problem of whether or not "one can hear the shape of a drum".
| Author | : David Eric Edmunds |
| Publisher | : Oxford University Press |
| Total Pages | : 610 |
| Release | : 2018 |
| Genre | : Mathematics |
| ISBN | : 0198812051 |
Download Spectral Theory and Differential Operators Book in PDF, Epub and Kindle
This book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators".The original book was a cutting edge account of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.
| Author | : Fedor S. Rofe-Beketov |
| Publisher | : World Scientific |
| Total Pages | : 466 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 9812703454 |
Download Spectral Analysis of Differential Operators Book in PDF, Epub and Kindle
This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic SchrAdinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals). The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators."
| Author | : M.A. Shubin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 296 |
| Release | : 2011-06-28 |
| Genre | : Mathematics |
| ISBN | : 3642565794 |
Download Pseudodifferential Operators and Spectral Theory Book in PDF, Epub and Kindle
I had mixed feelings when I thought how I should prepare the book for the second edition. It was clear to me that I had to correct all mistakes and misprints that were found in the book during the life of the first edition. This was easy to do because the mistakes were mostly minor and easy to correct, and the misprints were not many. It was more difficult to decide whether I should update the book (or at least its bibliography) somehow. I decided that it did not need much of an updating. The main value of any good mathematical book is that it teaches its reader some language and some skills. It can not exhaust any substantial topic no matter how hard the author tried. Pseudodifferential operators became a language and a tool of analysis of partial differential equations long ago. Therefore it is meaningless to try to exhaust this topic. Here is an easy proof. As of July 3, 2000, MathSciNet (the database of the American Mathematical Society) in a few seconds found 3695 sources, among them 363 books, during its search for "pseudodifferential operator". (The search also led to finding 963 sources for "pseudo-differential operator" but I was unable to check how much the results ofthese two searches intersected). This means that the corresponding words appear either in the title or in the review published in Mathematical Reviews.
| Author | : Michael Ruzhansky |
| Publisher | : Chapman & Hall/CRC |
| Total Pages | : 0 |
| Release | : 2020 |
| Genre | : Mathematics |
| ISBN | : 9781138360716 |
Download Spectral Geometry of Partial Differential Operators Book in PDF, Epub and Kindle
Access; Differential; Durvudkhan; Geometry; Makhmud; Michael; OA; Open; Operators; Partial; Ruzhansky; Sadybekov; Spectral; Suragan.
| Author | : V. A. Yurko |
| Publisher | : VSP |
| Total Pages | : 324 |
| Release | : 2002-01-01 |
| Genre | : Mathematics |
| ISBN | : 9789067643559 |
Download Method of Spectral Mappings in the Inverse Problem Theory Book in PDF, Epub and Kindle
Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural science. This monograph deals with inverse problems of spectral analysis for ordinary differential equations and aims to present the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory.The book consists of three chapters and opens with the method of spectral mappings, presented in the simplest version for the Sturm-Liouville operator. The second chapter deals with the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval. In this chapter the author introduces the so-called Weyl matrix, which is a generalization of the classical Weyl function for the selfadjoint second-order differential operator. The last chapter contains a study on inverse spectral problems for differential equations with nonlinear dependence on the spectral parameter.This monograph will be of value and interest to specialists in the field of inverse problems for differential equations.
| Author | : Olaf Post |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 444 |
| Release | : 2012-01-06 |
| Genre | : Mathematics |
| ISBN | : 3642238394 |
Download Spectral Analysis on Graph-like Spaces Book in PDF, Epub and Kindle
Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new tools such as norm convergence of operators acting in different Hilbert spaces, an extension of the concept of boundary triples to partial differential operators, and an abstract definition of resonances via boundary triples. These tools are formulated in an abstract framework, independent of the original problem of graph-like spaces, so that they can be applied in many other situations where the spaces are perturbed.
