Spectral And Scattering Theory For Second Order Partial Differential Operators
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Author |
: Kiyoshi Mochizuki |
Publisher |
: CRC Press |
Total Pages |
: 131 |
Release |
: 2017-06-01 |
ISBN-10 |
: 9781351648943 |
ISBN-13 |
: 1351648942 |
Rating |
: 4/5 (43 Downloads) |
Synopsis Spectral and Scattering Theory for Second Order Partial Differential Operators by : Kiyoshi Mochizuki
The book is intended for students of graduate and postgraduate level, researchers in mathematical sciences as well as those who want to apply the spectral theory of second order differential operators in exterior domains to their own field. In the first half of this book, the classical results of spectral and scattering theory: the selfadjointness, essential spectrum, absolute continuity of the continuous spectrum, spectral representations, short-range and long-range scattering are summarized. In the second half, recent results: scattering of Schrodinger operators on a star graph, uniform resolvent estimates, smoothing properties and Strichartz estimates, and some applications are discussed.
Author |
: Kiyoshi Mochizuki |
Publisher |
: CRC Press |
Total Pages |
: 232 |
Release |
: 2017-06-01 |
ISBN-10 |
: 9781498756037 |
ISBN-13 |
: 1498756034 |
Rating |
: 4/5 (37 Downloads) |
Synopsis Spectral and Scattering Theory for Second Order Partial Differential Operators by : Kiyoshi Mochizuki
The book is intended for students of graduate and postgraduate level, researchers in mathematical sciences as well as those who want to apply the spectral theory of second order differential operators in exterior domains to their own field. In the first half of this book, the classical results of spectral and scattering theory: the selfadjointness, essential spectrum, absolute continuity of the continuous spectrum, spectral representations, short-range and long-range scattering are summarized. In the second half, recent results: scattering of Schrodinger operators on a star graph, uniform resolvent estimates, smoothing properties and Strichartz estimates, and some applications are discussed.
Author |
: I.W. Knowles |
Publisher |
: Elsevier |
Total Pages |
: 401 |
Release |
: 1981-01-01 |
ISBN-10 |
: 9780080871660 |
ISBN-13 |
: 0080871666 |
Rating |
: 4/5 (60 Downloads) |
Synopsis Spectral Theory of Differential Operators by : I.W. Knowles
Spectral Theory of Differential Operators
Author |
: Hiroshi Isozaki |
Publisher |
: Springer Nature |
Total Pages |
: 130 |
Release |
: 2020-09-26 |
ISBN-10 |
: 9789811581991 |
ISBN-13 |
: 9811581991 |
Rating |
: 4/5 (91 Downloads) |
Synopsis Inverse Spectral and Scattering Theory by : Hiroshi Isozaki
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.
Author |
: |
Publisher |
: Elsevier |
Total Pages |
: 219 |
Release |
: 2011-09-21 |
ISBN-10 |
: 9780080871240 |
ISBN-13 |
: 0080871240 |
Rating |
: 4/5 (40 Downloads) |
Synopsis Spectral Theory and Asymptotics of Differential Equations by :
Spectral Theory and Asymptotics of Differential Equations
Author |
: Fedor S. Rofe-Beketov |
Publisher |
: World Scientific |
Total Pages |
: 466 |
Release |
: 2005 |
ISBN-10 |
: 9789812703453 |
ISBN-13 |
: 9812703454 |
Rating |
: 4/5 (53 Downloads) |
Synopsis Spectral Analysis of Differential Operators by : Fedor S. Rofe-Beketov
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 |
: David Edmunds |
Publisher |
: Oxford University Press |
Total Pages |
: |
Release |
: 2018-05-03 |
ISBN-10 |
: 9780192540102 |
ISBN-13 |
: 0192540106 |
Rating |
: 4/5 (02 Downloads) |
Synopsis Spectral Theory and Differential Operators by : David Edmunds
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 |
: |
Publisher |
: |
Total Pages |
: |
Release |
: 1991 |
ISBN-10 |
: 0387546774 |
ISBN-13 |
: 9780387546773 |
Rating |
: 4/5 (74 Downloads) |
Synopsis Partial Differential Equations by :
Author |
: M. Sh Birman |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 348 |
Release |
: 1999 |
ISBN-10 |
: 0821813870 |
ISBN-13 |
: 9780821813874 |
Rating |
: 4/5 (70 Downloads) |
Synopsis Differential Operators and Spectral Theory by : M. Sh Birman
This volume contains a collection of original papers in mathematical physics, spectral theory and differential equations. The papers are dedicated to the outstanding mathematician, Professor M Sh Birman, on the occasion of his 70th birthday. Contributing authors are leading specialists and close professional coleagues of Birman. The main topics discussed are spectral and scattering theory of differential operators , trace formulas, and boundary value problems for PDEs. Several papers are devoted to the magnetic Schrodinger operator, which is within Birman's current scopeof interests and recently has been studied extensively. Included is a detailed survey of his mathematical work and an updated list of his publications. This book is aimed at graduate students and specialists in the above-mentioned branches of mathematics and theoretical physicists. The biographical section will be of interest to readers concerned with the scientific activities of Birman and the history of those branches of analysis and spectral theory where his contributions were important and often decisive.
Author |
: W.N. Everitt |
Publisher |
: Springer |
Total Pages |
: 338 |
Release |
: 2006-11-15 |
ISBN-10 |
: 9783540374442 |
ISBN-13 |
: 3540374442 |
Rating |
: 4/5 (42 Downloads) |
Synopsis Spectral Theory and Differential Equations by : W.N. Everitt