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Non-consistent approximations of self-adjoint eigenproblems: Application to the supercell method
Non-consistent approximations self-adjoint eigenproblems Functional Analysis
2012/5/24
In this article, we introduce a general theoretical framework to analyze non-consistent approximations of the discrete eigenmodes of a self-adjoint operator. We focus in particular on the discrete eig...
Constructing all self-adjoint matrices with prescribed spectrum and diagonal
Schur-Horn interlacing majorization frames
2011/9/1
Abstract: The Schur-Horn Theorem states that there exists a self-adjoint matrix with a given spectrum and diagonal if and only if the spectrum majorizes the diagonal. Though the original proof of this...
On the Spectra and Pseudospectra of a Class of Non-Self-Adjoint Random Matrices and Operators
Pseudospectra Non-Self-Adjoint Random Matrices Operators
2011/8/22
Abstract: In this paper we develop and apply methods for the spectral analysis of non-self-adjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous determini...
Spectral estimates for resolvent differences of self-adjoint elliptic operators
Spectral estimates resolvent differences
2011/2/24
The notion of quasi boundary triples and their Weyl functions is an abstract concept to treat spectral and boundary value problems for elliptic partial differential equations.
Symmetry preserving self-adjoint extensions of Schrödinger operators with singular potentials
Symmetry preserving self-adjoint extensions Schrö dinger operators singular potentials
2011/1/21
We develop a general technique for finding self-adjoint extensions of a symmetric operator that respect a given set of its symmetries. Prob-lems of this type naturally arise when considering two- and ...
Almost commuting self-adjoint matrices --- the real and self-dual cases
self-adjoint matrices self-dual cases
2011/2/21
We show that a pair of almost commuting self-adjoint, symmetric ma-trices are close to commuting self-adjoint, symmetric matrices (in a uni-form way).
Growth Estimates for Orbits of Self Adjoint Groups
Growth Estimates Orbits of Self Adjoint Groups
2011/1/21
Let G denote a closed, connected, self adjoint, noncompact subgroup of GL(n,R), and let dR
and dL denote respectively the right and left invariant Riemannian metrics defined by the canonical inner pr...
Weyl theorems for the polluted set of self-adjoint operators in Galerkin approximations
Weyl theorems self-adjoint operators Galerkin approximations
2010/11/22
Let A be a self-adjoint operator on a separable Hilbert space H and let (L_n) be a sequence of finite dimensional subspaces of the domain of A, approximating H in the large n limit. Denote by A_n the...
A mini-max problem for self-adjoint Toeplitz matrices
Toeplitz matrix Toeplitz operator trigonometric moment problems
2010/12/6
We study a minimum problem and associated maximum problem for finite, complex, self-adjoint Toeplitz matrices. If A is such a matrix, of size (N + 1)-by-(N + 1), we identify A with the operator it rep...
On a class of $J$-self-adjoint operators with empty resolvent set
Elliptic curve Elliptic divisibility sequence Primitive divisor
2010/11/30
We establish conditions necessary for the n-th element of any elliptic divisibility sequence generated by points on Ea : y2 = x3+ax to not have a primitive divisor. As a consequence of this, along wit...
Self-adjoint extensions and spectral analysis in the generalized Kratzer problem
Self-adjoint extensions spectral analysis generalized Kratzer problem
2010/12/13
We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional nonrelativistic motion of a particle in the potential field V (x) = g1x−1 + g2x−2, x 2 R+ = [0,1) .Fo...
lower bound of the first eigenvalue of certain self-adjoint elliptic operators on manifolds containing long necks
lower bound manifolds containing long necks certain self-adjoint elliptic operators
2010/3/5
In this note, under certain regularity and transversality conditions we obtain a sharp lower bound of the first eigenvalue for certain self-adjoint elliptic operators on manifolds with long necks. Thi...
A new technique is proposed for the analysis of shape optimization problems. The technique uses the asymptotic analysis of boundary value problems in singularly perturbed geometrical domains. The asym...
On the Norm of a Self-Adjoint Operator and a New Bilinear Integral Inequality
norm self-adjoint bilinear inequality Beta function
2007/12/11
In this paper, the expression of the norm of a self-adjoint integral operator $T:$ $% L^{2}(0,\infty )\rightarrow L^{2}(0,\infty )$ is obtained. As applications, a new bilinear integral inequality wit...
Self-Adjoint Boundary Value Problems on Time Scales and Symmetric Green's Functions
Time scales self-adjoint differential expressions self-adjoint boundary conditions
2010/2/26
In this note, higher order self-adjoint differential expressions on time scales, and associated with them self-adjoint boundary conditions, are discussed. The symmetry peoperty of the corresponding Gr...