Elliptic operators with unbounded coefficients: construction of a maximal dissipative extension

We prove maximal dissipativity of some dissipative systems in where is an invariant measure. Received May 23, 2000; accepted June 10, 2000.     

A control problem governed by a second-order differential inclusion

This article studies some Bolza-type problems governed by second-order differential inclusions with two boundary conditions, where the controls are Young measures.     

Global Continuity of the Integrated Density of States for Random Landau Hamiltonians

Abstract

We prove that the integrated density of states (IDS) for the randomly perturbed Landau Hamiltonian is Hölder continuous at all energies with any Hölder exponent 0 < q < 1. The random Anderson-type potential is constructed with a nonnegative, compactly supported single-site potential u. The distribution of the iid random variables is required to be absolutely continuous with a bounded, compactly supported density. This extends a previous result Combes et al. [Combes, J. M., Hislop, P. D., Klopp, F. (2003a). Hölder continuity of the integrated density of states for some random operators at all energies. Int. Math. Res. Notices 2003: 179--209] that was restricted to constant magnetic fields having rational flux through the unit square. We also prove that the IDS is Hölder continuous as a function of the nonzero magnetic field strength.     

On solutions of quasilinear elliptic inequalities containing terms with lower-order derivatives

We obtain estimates and blow-up conditions for solutions of quasilinear elliptic inequalities containing terms with lower-order derivatives.     

平移不变线性算子的连续性

利用一类紧ａｂｅｌｉａｎ群Ｇ上的函数空间Ｌ２（Ｇ）上以及Ｄ（Ｒ）上平移不变线性泛函的自动连续性并结合闭图象定理证明这些空间上的平移不变线性算子连续。     

Algebras of Approximation Sequences: Finite Sections of Band-Dominated Operators

We develop the stability theory for the finite section method for general band-dominated operators on l^p spaces over Z^k. The main result says that this method is stable if and only if each member of a whole family of operators – the so-called limit operators of the method – is invertible and if the norms of these inverses are uniformly bounded.     

Weighted approximation of continuous functions by sequences of linear positive operators

In this work we obtain, under suitable conditions, theorems of Korovkin type for spaces with different weight, composed of continuous functions defined on unbounded regions. These results can be seen as an extension of theorems by Gadjiev in [4] and [5].     

An Approximation Criterion for Essential Self-adjointness of Dirichlet Operators on Certain Banach Spaces

We establish an approximation criterion for essential self-adjointness of Dirichlet operators with nonconstant diffusion part on certain Banach spaces.     

Composition operators on Hardy spaces of Riemann surfaces

Our purpose is to define composition operators acting upon Hardy spaces of Riemann surfaces. In terms of counting functions related to analytic self-map on Riemann surfaces, the boundedness and compactness are characterized.