Results 41 to 50 of about 873 (53)
Sharp boundary estimates for elliptic operators [PDF]
arXiv, 1998 We prove sharp L^2 boundary decay estimates for the eigenfunctions of certain second order elliptic operators acting in a bounded region, and of their first order space derivatives, using only the Hardy inequality. We then deduce bounds on the change of the eigenvalues when the region is reduced slightly in size, subject to DBCs.
arxiv
Spectral Instability for Some Schroedinger Operators [PDF]
arXiv, 1998 We define the concept of instability index of an isolated eigenvalue of a non-self-adjoint operator, and prove some of its general properties. We also describe a stable procedure for computing this index for Schroedinger operators in one dimension, and apply it to the complex resonances of a typical operator with a dilation analytic potential.
arxiv
Bounds on complex eigenvalues and resonances [PDF]
arXiv, 1999 We obtain bounds on the complex eigenvalues of non-self-adjoint Schr\"odinger operators with complex potentials, and also on the complex resonances of self-adjoint Schr\"odinger operators. Our bounds are compared with numerical results, and are seen to provide useful information.
arxiv
Le spectre et la torsion analytique des fibres en droites sur les tores complexes [PDF]
arXiv, 2001 The spectrum of the Laplace-Dolbeault operator for any line bundle with parallel curvature on a flat complex torus is computed. The Ray-Singer analytic torsion is then deduced, generalizing thus Bost's result for ample line bundles and Ray-Singer's ones for flat bundles, of which we a geometric interpretation is given.
arxiv
Another Simple Proof of a Theorem of Chandler Davis [PDF]
arXiv, 2002 In 1957, Chandler Davis proved that unitarily invariant convex functions on the space of hermitian matrices are precisely those which are convex and symmetrically invariant on the set of diagonal matrices. We give a simple perturbation theoretic proof of this result. (Davis' argument was also very short, though based on completely different ideas).
arxiv
Spectral pollution and second order relative spectra for self-adjoint operators [PDF]
arXiv, 2002 We consider the phenomenon of spectral pollution arising in calculation of spectra of self-adjoint operators by projection methods. We suggest a strategy of dealing with spectral pollution by using the so-called second order relative spectra. The effectiveness of the method is illustrated by a detailed analysis of two model examples.
arxiv
Szegö limit theorems for operators with almost periodic diagonals [PDF]
arXiv, 2006 The classical Szeg\"o theorems study the asymptotic behaviour of the determinants of the finite sections $P_n T(a) P_n$ of Toeplitz operators, i.e., of operators which have constant entries along each diagonal. We generalize these results to operators which have almost periodic functions on their diagonals.
arxiv
Sharp Lieb-Thirring Inequalities in High Dimensions [PDF]
arXiv, 1999 We show how a matrix version of the Buslaev-Faddeev-Zakharov trace formulae for a one-dimensional Schr\"odinger operator leads to Lieb-Thirring inequalities with sharp constants $L^{cl}_{\gamma,d}$ with $\gamma\ge 3/2$ and arbitrary $d\ge 1$. (revised, to appear in Acta Math)
arxiv
Some generalizations of Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities [PDF]
arXiv, 2008 The paper is withdrawn by the authors and replaced be an improved and extended version arxiv: 0812 ...
arxiv
On the comparison of the Dirichlet and Neumann counting functions [PDF]
arXiv, 2008 The aim of the paper is to show that L. Friedlander's results on the relation between Dirichlet and Neumann counting functions (Arch. Ration. Mech. Anal. 116, 1991) remain valid in abstract setting.
arxiv