Abstract The generalized Schwarz algorithm for a class of elliptic quasi-variational inequalities related to impulse control problems is studied in this paper. principal result prove the error estimate $L^{\infty}$ L ∞ -norm m subdomains with overlapping nonmatching gri...

‎Given a frame of a separable Hilbert space $H$‎, ‎we present some‎ ‎iterative methods for solving an operator equation $Lu=f$‎, ‎where $L$ is a bounded‎, ‎invertible and symmetric‎ ‎operator on $H$‎. ‎We present some algorithms‎ ‎based on the knowledge of frame bounds‎, ‎Chebyshev method and conjugate gradient method‎, ‎in order to give some‎ ‎approximated solutions to the problem‎. ‎Then we i...

This paper is devoted to the convergence rate estimate for the method of successive subspace corrections applied to symmetric and positive semidefinite (singular) problems. In a general Hilbert space setting, a convergence rate identity is obtained for the method of subspace corrections in terms of the subspace solvers. As an illustration, the new abstract theory is used to show uniform converg...

Consider a class of skew product transformations consisting of an ergodic or a periodic transformation on a probability space (M,B, μ) in the base and a semigroup of transformations on another probability space (Ω,F , P ) in the fibre. Under suitable mixing conditions for the fibre transformation, we show that the properties ergodicity, weakly mixing, and strongly mixing are passed on from the ...

It is shown that the Vitali convergence theorem remains valid for the -upper integral. Using this result we prove completeness of the space L( ) with respect to the k kp-upper norm for 1 p < 1 , describe convergence of its elements in terms of the space L( ) for 1 p < 1 , give a necessary and sufficient condition for a sequence from L( ) to converge in the k kp-upper norm to a function from L( ...

This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result for the mentioned systems of equations are obtained as an application of a basic approximation result, which is formulated entirely in terms of usual real va...

In this paper we obtain almost sure convergence theorems for vectorvalued uniform amarts and C-sequences without assuming the Radon-Nikodym Property. Specifically, it is shown that if a limit exists in a weak sense for these martingale generalizations, then a.s. scalar and strong convergence follow. These results lead to some new versions of the Ito-Nisio theorem. Convergence results for random...

The spectral shift function ξL(E) for a Schrödinger operator restricted to a finite cube of length L in multi-dimensional Euclidean space, with Dirichlet boundary conditions, counts the number of eigenvalues less than or equal to E ∈ R created by a perturbation potential V . We study the behavior of this function ξL(E) as L→∞ for the case of a compactly-supported and bounded potential V . After...

In this paper, using entropy techniques, we study the rate of convergence of nonnegative solutions of a simple scalar conservation law to their asymptotic states in a weighted L norm. After an appropriate rescaling and for a well chosen weight, we obtain an exponential rate of convergence to a stationary solution. Written in the original coordinates,this provides intermediate asymptotics estima...