Spectral Theory Of Non Self Adjoint Two Point Differential Operators PDF Download
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| Author | : John Locker |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 266 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821820494 |
Download Spectral Theory of Non-Self-Adjoint Two-Point Differential Operators Book in PDF, ePub and Kindle
Develops the spectral theory of an nth order non-self-adjoint two- point differential operator L in the complex Hilbert space L2[0,1]. The differential operator L is determined by an nth order formal differential l and by n linearly independent boundary values B1,.,Bn. Locker first lays the foundations of the spectral theory for closed linear operators and Fredholm operators in Hilbert spaces before developing the spectral theory of the differential operator L. The book is a sequel to Functional analysis and two-point differential operators, 1986. Annotation copyrighted by Book News, Inc., Portland, OR.
| Author | : V.A. Il'in |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 403 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461517559 |
Download Spectral Theory of Differential Operators Book in PDF, ePub and Kindle
In this fully-illustrated textbook, the author examines the spectral theory of self-adjoint elliptic operators. Chapters focus on the problems of convergence and summability of spectral decompositions about the fundamental functions of elliptic operators of the second order. The author's work offers a novel method for estimation of the remainder term of a spectral function and its Riesz means without recourse to the traditional Carleman technique and Tauberian theorem apparatus.
| Author | : Erich Müller-Pfeiffer |
| Publisher | : Ellis Horwood |
| Total Pages | : 256 |
| Release | : 1981 |
| Genre | : Differential operators |
| ISBN | : |
Download Spectral Theory of Ordinary Differential Operators Book in PDF, ePub and Kindle
| Author | : Johannes Sjöstrand |
| Publisher | : Springer |
| Total Pages | : 496 |
| Release | : 2019-05-17 |
| Genre | : Mathematics |
| ISBN | : 3030108198 |
Download Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations Book in PDF, ePub and Kindle
The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago. In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book. Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.
| Author | : E. Brian Davies |
| Publisher | : Cambridge University Press |
| Total Pages | : 198 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 9780521587105 |
Download Spectral Theory and Differential Operators Book in PDF, ePub and Kindle
This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on partial differential operators.
| Author | : R. Mennicken |
| Publisher | : Gulf Professional Publishing |
| Total Pages | : 536 |
| Release | : 2003-06-26 |
| Genre | : Mathematics |
| ISBN | : 9780444514479 |
Download Non-Self-Adjoint Boundary Eigenvalue Problems Book in PDF, ePub and Kindle
The 'North-Holland Mathematics Studies' series comprises a set of cutting-edge monographs and studies. This volume explores non-self-adjoint boundary eigenvalue problems for first order systems of ordinary differential equations and n-th order scalar differential equations.
| 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 | : Nelson Dunford |
| Publisher | : John Wiley & Sons |
| Total Pages | : 1092 |
| Release | : 1988-02-23 |
| Genre | : Mathematics |
| ISBN | : 0471608475 |
Download Linear Operators, Part 2 Book in PDF, ePub and Kindle
This classic text, written by two notable mathematicians, constitutes a comprehensive survey of the general theory of linear operations, together with applications to the diverse fields of more classical analysis. Dunford and Schwartz emphasize the significance of the relationships between the abstract theory and its applications. This text has been written for the student as well as for the mathematician—treatment is relatively self-contained. This is a paperback edition of the original work, unabridged, in three volumes.
| Author | : John Locker |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 194 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821841718 |
Download Eigenvalues and Completeness for Regular and Simply Irregular Two-Point Differential Operators Book in PDF, ePub and Kindle
In this monograph the author develops the spectral theory for an $n$th order two-point differential operator $L$ in the Hilbert space $L2[0,1]$, where $L$ is determined by an $n$th order formal differential operator $\ell$ having variable coefficients and by $n$ linearly independent boundary values $B 1, \ldots, B n$. Using the Birkhoff approximate solutions of the differential equation $(\rhon I - \ell)u = 0$, the differential operator $L$ is classified as belonging to one of threepossible classes: regular, simply irregular, or degenerate irregular. For the regular and simply irregular classes, the author develops asymptotic expansions of solutions of the differential equation $(\rhon I - \ell)u = 0$, constructs the characteristic determinant and Green's function,characterizes the eigenvalues and the corresponding algebraic multiplicities and ascents, and shows that the generalized eigenfunctions of $L$ are complete in $L2[0,1]$. He also gives examples of degenerate irregular differential operators illustrating some of the unusual features of this class.
| Author | : Boris Moiseevich Levitan |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 542 |
| Release | : 1975 |
| Genre | : Mathematics |
| ISBN | : 082181589X |
Download Introduction to spectral theory: selfadjoint ordinary differential operators Book in PDF, ePub and Kindle
Presents a monograph that is devoted to the spectral theory of the Sturm- Liouville operator and to the spectral theory of the Dirac system. This book concerns with nth order operators that can serve as simply an introduction to this domain. It includes a chapter that discusses this theory.
