A Method for Approximating the Eigenvalues of Non Self-adjoint Ordinary Differential Operators
Title | A Method for Approximating the Eigenvalues of Non Self-adjoint Ordinary Differential Operators PDF eBook |
Author | John E. Osborn |
Publisher | |
Pages | 196 |
Release | 1979 |
Genre | Differential operators |
ISBN |
A method for approximating the eigenvalues of non self-adjoint differential operators
Title | A method for approximating the eigenvalues of non self-adjoint differential operators PDF eBook |
Author | John E. Osborn |
Publisher | |
Pages | 56 |
Release | 1971 |
Genre | |
ISBN |
Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems
Title | Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems PDF eBook |
Author | Xuefeng Liu |
Publisher | Springer Nature |
Pages | 139 |
Release | |
Genre | |
ISBN | 9819735777 |
Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations
Title | Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations PDF eBook |
Author | Johannes Sjöstrand |
Publisher | Springer |
Pages | 496 |
Release | 2019-05-17 |
Genre | Mathematics |
ISBN | 3030108198 |
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.
Variational Methods for Eigenvalue Approximation
Title | Variational Methods for Eigenvalue Approximation PDF eBook |
Author | H. F. Weinberger |
Publisher | SIAM |
Pages | 165 |
Release | 1974-01-01 |
Genre | Mathematics |
ISBN | 9781611970531 |
Provides a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasizes their relationships. A mapping principle is presented to connect many of the methods. The eigenvalue problems studied are linear, and linearization is shown to give important information about nonlinear problems. Linear vector spaces and their properties are used to uniformly describe the eigenvalue problems presented that involve matrices, ordinary or partial differential operators, and integro-differential operators.
Variational Methods for Eigenvalue Approximation
Title | Variational Methods for Eigenvalue Approximation PDF eBook |
Author | Hans F. Weinberger |
Publisher | SIAM |
Pages | 178 |
Release | 1974 |
Genre | Mathematics |
ISBN |
Provides a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasizes their relationships.
Rate of Convergence Estimates for Non-selfadjoint Eigenvalue Approximations
Title | Rate of Convergence Estimates for Non-selfadjoint Eigenvalue Approximations PDF eBook |
Author | James H. Bramble |
Publisher | |
Pages | 58 |
Release | 1972 |
Genre | Eigenvalues |
ISBN |
In the paper a general approximation theory for the eigenvalues and corresponding subspaces of generalized eigenfunctions of a certain class of compact operators is developed. This theory is then used to obtain rate of convergence estimates for the errors which arise when the eigenvalues of non-selfadjoint elliptic partial differential operators are approximated by Rayleigh-Ritz-Galerkin type methods using finite dimensional spaces of trial functions, e.g. spline functions. The approximation methods include several in which the functions in the space of trial functions are not required to satisfy any boundary conditions. (Author).