Inverse Spectral Problems For Linear Differential Operators And Their Applications PDF Download
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Author | : V A Yurko |
Publisher | : CRC Press |
Total Pages | : 272 |
Release | : 2000-01-18 |
Genre | : Mathematics |
ISBN | : 1482287439 |
Download Inverse Spectral Problems for Linear Differential Operators and Their Applications Book in PDF, ePub and Kindle
Aims to construct the inverse problem theory for ordinary non-self-adjoint differential operators of arbitary order on the half-line and on a finite interval. The book consists of two parts: in the first part the author presents a general inverse problem of recovering differential equations with integrable coefficients when the behaviour of the spe
Author | : Natalia Bondarenko |
Publisher | : |
Total Pages | : 0 |
Release | : 2024-08-02 |
Genre | : Mathematics |
ISBN | : 9783725815951 |
Download Direct and Inverse Spectral Problems for Ordinary Differential and Functional-Differential Operators Book in PDF, ePub and Kindle
This reprint contains a collection of research papers on spectral theory for differential and functional differential operators. Spectral theory plays a fundamental role in mathematics and has applications in various fields of science and engineering, e.g., in quantum and classical mechanics, geophysics, acoustics, and electronics. The collection includes recent studies on a variety of topics such as analytical and numerical methods for solving direct and inverse spectral problems, new developments in the theory of partial differential equations, pseudo-differential equations with fractional derivatives, asymptotical analysis for solutions of differential equations, spectral theory for abstract operators in Hilbert spaces, and inverse nodal problems.
Author | : G. Freiling |
Publisher | : Nova Biomedical Books |
Total Pages | : 324 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : |
Download Inverse Sturm-Liouville Problems and Their Applications Book in PDF, ePub and Kindle
This book presents the main results and methods on inverse spectral problems for Sturm-Liouville differential operators and their applications. 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 sciences. Inverse problems also play an important role in solving non-linear evolution equations in mathematical physics. Interest in this subject has been increasing permanently because of the appearance of new important applications, resulting in intensive study of inverse problem theory all over the world.
Author | : Vacheslav A. Yurko |
Publisher | : Walter de Gruyter |
Total Pages | : 316 |
Release | : 2013-10-10 |
Genre | : Mathematics |
ISBN | : 3110940965 |
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 is devoted to inverse problems of spectral analysis for ordinary differential equations. Its aim ist 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: In Chapter 1 the method of spectral mappings is presented in the simplest version for the Sturm-Liouville operator. In Chapter 2 the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval, is considered. In Chapter 3 inverse spectral problems for differential operators with nonlinear dependence on the spectral parameter are studied.
Author | : V. A. Yurko |
Publisher | : |
Total Pages | : 316 |
Release | : 2002 |
Genre | : Inverse problems (Differential equations) |
ISBN | : 9783110631210 |
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 is devoted to inverse problems of spectral analysis for ordinary differential equations. Its aim ist 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: In Chapter 1 the method of spectral mappings is presented in the simplest version for the Sturm-Liouville operator. In Chapter 2 the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval, is considered. In Chapter 3 inverse spectral problems for differential operators with nonlinear dependence on the spectral parameter are studied.
Author | : Hiroshi Isozaki |
Publisher | : American Mathematical Soc. |
Total Pages | : 258 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821834215 |
Download Inverse Problems and Spectral Theory Book in PDF, ePub and Kindle
This volume grew out of a workshop on spectral theory of differential operators and inverse problems held at the Research Institute for Mathematical Sciences (Kyoto University). The gathering of nearly 100 participants at the conference suggests the increasing interest in this field of research. The focus of the book is on spectral theory for differential operators and related inverse problems. It includes selected topics from the following areas: electromagnetism, elasticity, the Schrodinger equation, differential geometry, and numerical analysis. The material is suitable for graduate students and researchers interested in inverse problems and their applications.
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 | : 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 | : Boris Moiseevič Levitan |
Publisher | : VSP |
Total Pages | : 258 |
Release | : 1987 |
Genre | : Mathematics |
ISBN | : 9789067640558 |
Download Inverse Sturm-Liouville Problems Book in PDF, ePub and Kindle
The interest in inverse problems of spectral analysis has increased considerably in recent years due to the applications to important non-linear equations in mathematical physics. This monograph is devoted to the detailed theory of inverse problems and methods of their solution for the Sturm-Liouville case. Chapters 1--6 contain proofs which are, in many cases, very different from those known earlier. Chapters 4--6 are devoted to inverse problems of quantum scattering theory with attention being focused on physical applications. Chapters 7--11 are based on the author's recent research on the theory of finite- and infinite-zone potentials. A chapter discussing the applications to the Korteweg--de Vries problem is also included. This monograph is important reading for all researchers in the field of mathematics and physics.
Author | : Michael Ruzhansky |
Publisher | : CRC Press |
Total Pages | : 366 |
Release | : 2020-02-07 |
Genre | : Mathematics |
ISBN | : 0429780575 |
Download Spectral Geometry of Partial Differential Operators Book in PDF, ePub and Kindle
The aim of Spectral Geometry of Partial Differential Operators is to provide a basic and self-contained introduction to the ideas underpinning spectral geometric inequalities arising in the theory of partial differential equations. Historically, one of the first inequalities of the spectral geometry was the minimization problem of the first eigenvalue of the Dirichlet Laplacian. Nowadays, this type of inequalities of spectral geometry have expanded to many other cases with number of applications in physics and other sciences. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they produce a priori bounds for spectral invariants of (partial differential) operators on arbitrary domains. Features: Collects the ideas underpinning the inequalities of the spectral geometry, in both self-adjoint and non-self-adjoint operator theory, in a way accessible by anyone with a basic level of understanding of linear differential operators Aimed at theoretical as well as applied mathematicians, from a wide range of scientific fields, including acoustics, astronomy, MEMS, and other physical sciences Provides a step-by-step guide to the techniques of non-self-adjoint partial differential operators, and for the applications of such methods. Provides a self-contained coverage of the traditional and modern theories of linear partial differential operators, and does not require a previous background in operator theory.