Juan Bory-Reyes, Diana Barseghyan, Baruch Schneider
In this paper we derive Lieb-Thirring estimates for eigenvalues of Dirichlet Laplacians below the threshold of the essential spectrum on asymptotically Archimedean spiral-shaped regions.
In this paper we consider the one-dimensional Schrodinger operator L(q) with a periodic real and locally integrable potential q. We study the bands and gaps in the spectrum and explicitly write out the first and second terms of the asymptotic formulas for the length of the gaps in the spectrum.
The paper is concerned with the completeness property of root functions of the Dirac operator with summable complexvalued potential and non-regular boundary conditions. We also obtain explicit form for the fundamental solution system of the considered operator.
In this paper we consider the continuity of the band functions and Bloch functions of the differential operators generated by the differential expressions with periodic matrix coefficients.
We consider the elliptical range theorems for the Davis--Wielandt shell, the numerical range, and the conformal range in terms of and related to their quadratic representations. The emphasis is on exposing a variety of elementary approaches.
The center of mass of a finite measure with respect to a radially increasing weight is shown to exist, be unique, and depend continuously on the measure.
We show that if a list of nonzero complex numbers $σ=(λ_1,λ_2,\ldots,λ_k)$ is the nonzero spectrum of a diagonalizable nonnegative matrix, then $σ$ is the nonzero spectrum of a diagonalizable nonnegative matrix of order $k+k^2.$
We consider the 3-dimensional Stark operator perturbed by a complex-valued potential. We obtain an estimate for the number of eigenvalues of this operator as well as for the sum of imaginary parts of eigenvalues situated in the upper half-plane.
We define a generalized Berezin transforms on line bundle over the complex hyperbolic space and we give it as a functions of the G-invariant laplacian on the line bundles.
We describe the Krein extension of minimal operator associated with the expression A:=(-1)^n*d^(2n)/dx^(2n) on a finite interval (a,b) in terms of boundary conditions. All non-negative extensions of the operator A as well as extensions with a finite number of negative squares are described.
In this paper we provide new asymptotic estimates of various spectral quantities of Zakharov-Shabat operators on the circle. These estimates are uniform on bounded subsets of potentials in Sobolev spaces.
Different estimates for the norm of the self-commutator of a Hilbert space operator are proposed. Particularly, this norm is bounded from above by twice of the area of the numerical range of the operator. An isoperimetric-type inequality is proved.
We describe a general approach for computing generators for elimination ideals associated with matrix and hypermatrix spectral decomposition constraints. We derive from these generators iterative procedures for approximating the spectral decomposition of matrices and hypermatrices.
The paper contains a simplified version of Stahl's proof of a conjecture of Bessis, Moussa and Villani on the trace of matrices A+tB with Hermitean A and B.
We discuss resonances for Schrödinger operators with compactly supported potentials on the line and the half-line. We estimate the sum of the negative power of all resonances and eigenvalues in terms of the norm of the potential and the diameter of its support. The proof is based on harmonic analysis and Carleson measures arguments.
The classical Szegö theorem can be stated in terms of the sequence of model spaces. In this article, we are interested in the generalization of the Szegö theorem in the case of the sequence of powers of finite Blaschke products.
In this article, we derive bounds for values of the global geometry of locally tessellating planar graphs, namely, the Cheeger constant and exponential growth, in terms of combinatorial curvatures. We also discuss spectral implications for the Laplacians.
We prove an explicit formula for the spectral expansions in $L^2(\R)$ generated by selfadjoint differential operators $$ (-1)^n\frac{d^{2n}}{dx^{2n}}+\sum\limits_{j=0}^{n-1}\frac{d^{j}}{dx^{j}} p_j(x)\frac{d^{j}}{dx^{j}},\quad p_j(x+π)=p_j(x),\quad x\in\R. $$
The Orr-Sommerfeld equation is a spectral problem which is known to play an important role in hydrodynamic stability. For an appropriate operator theoretical realization of the equation, we will determine the essential spectrum, and calculate an enclosure of the set of all eigenvalues by elementary analytical means.