Search results for "Spectral"
showing 10 items of 3116 documents
Notes on the subspace perturbation problem for off-diagonal perturbations
2014
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear; arXiv:1310.4360 (2013)] is adapted. It is shown that, in contrast to the case of general perturbations, the corresponding optimization problem can not be reduced to a finite-dimensional problem. A suitable choice of the involved parameters provides an upper bound for the solution of the optimization problem. In particular, this yields a rotation bound on the subspaces that is stronger than the previously known one from [J. Reine Angew. Math. (2013), DOI:10.1515/cre…
Hardy-Orlicz Spaces of conformal densities
2014
We define and prove characterizations of Hardy-Orlicz spaces of conformal densities.
Approximations of positive operators and continuity of the spectral radius III
1994
AbstractWe prove estimates on the speed of convergence of the ‘peripheral eigenvalues’ (and principal eigenvectors) of a sequence Tn of positive operators on a Banach lattice E to the peripheral eigenvalues of its limit operator T on E which is positive, irreducible and such that the spectral radius r(T) of T is a Riesz point of the spectrum of T (that is, a pole of the resolvent of T with a residuum of finite rank) under some conditions on the kind of approximation of Tn to T. These results sharpen results of convergence obtained by the authors in previous papers.
Toeplitz band matrices with small random perturbations
2021
We study the spectra of $N\times N$ Toeplitz band matrices perturbed by small complex Gaussian random matrices, in the regime $N\gg 1$. We prove a probabilistic Weyl law, which provides an precise asymptotic formula for the number of eigenvalues in certain domains, which may depend on $N$, with probability sub-exponentially (in $N$) close to $1$. We show that most eigenvalues of the perturbed Toeplitz matrix are at a distance of at most $\mathcal{O}(N^{-1+\varepsilon})$, for all $\varepsilon >0$, to the curve in the complex plane given by the symbol of the unperturbed Toeplitz matrix.
Analysis of geometric operators on open manifolds: A groupoid approach
2001
The first five sections of this paper are a survey of algebras of pseudodifferential operators on groupoids. We thus review differentiable groupoids, the definition of pseudodifferential operators on groupoids, and some of their properties. We use then this background material to establish a few new results on these algebras, results that are useful for the analysis of geometric operators on non-compact manifolds and singular spaces. The first step is to establish that the geometric operators on groupoids are in our algebras. This then leads to criteria for the Fredholmness of geometric operators on suitable non-compact manifolds, as well as to an inductive procedure to study their essentia…
Local Spectral Theory
2018
In this chapter we shall introduce an important property, defined for bounded linear operators on complex Banach spaces, the so-called single-valued extension property (SVEP).
Sign-indefinite second order differential operators on finite metric graphs
2012
The question of self-adjoint realizations of sign-indefinite second order differential operators is discussed in terms of a model problem. Operators of the type $-\frac{d}{dx} \sgn (x) \frac{d}{dx}$ are generalized to finite, not necessarily compact, metric graphs. All self-adjoint realizations are parametrized using methods from extension theory. The spectral and scattering theory of the self-adjoint realizations are studied in detail.
Some spectral mapping theorems through local spectral theory
2004
The spectral mapping theorems for Browder spectrum and for semi-Browder spectra have been proved by several authors [14], [29] and [33], by using different methods. We shall employ a local spectral argument to establish these spectral mapping theorems, as well as, the spectral mapping theorem relative to some other classical spectra. We also prove that ifT orT* has the single-valued extension property some of the more important spectra originating from Fredholm theory coincide. This result is extended, always in the caseT orT* has the single valued extension property, tof(T), wheref is an analytic function defined on an open disc containing the spectrum ofT. In the last part we improve a re…
Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems
2013
In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ1(Ω) for the p-Laplace operator (p > 1) in a Lipschitz bounded domain Ω in ℝn. Our estimate does not require any convexity assumption on Ω and it involves the best isoperimetric constant relative to Ω. In a suitable class of convex planar domains, our bound turns out to be better than the one provided by the Payne—Weinberger inequality.
A theoretical study of the low-lying excited states of thieno[3,4-b]pyrazine
2009
The low-lying electronic excited states of thieno[3,4-b]pyrazine have been studied using the multiconfigurational second-order perturbation CASPT2 theory with extended atomic natural orbital basis sets. The CASPT2 results allow for a full interpretation of the electronic absorption and emission spectra and provide valuable information for the rationalization of the experimental data. The nature, position, and intensity of the spectral bands have been analyzed in detail. A preliminary comparative study of the ground-state geometry of thieno[3,4-b]pyrazine has been performed at the coupled cluster single and doubles and density functional theory levels using a variety of correlation-consisten…