Quantitative estimates for interpolated operators by multidimensional method

Quantitative Estimates for the Finite Section Method

The finite section method is a classical scheme to approximate the solution of an infinite system of linear equations. We present quantitative estimates for the rate of the convergence of the finite section method on weighted `-spaces. Our approach uses recent results from the theory of Banach algebras of matrices with off-diagonal decay. Furthermore, we demonstrate that Banach algebra theory p...

Quantitative Global Estimates for Generalized Double Szasz-Mirakjan Operators

Operators for Multidimensional Aggregate Data

Copyright © 2003, Idea Group Inc. Copying or distributing in print or electronic forms without written permission of Idea Group Inc. is prohibited. ABSTRACT In this chapter the author proposes the different approaches for defining operators able to manipulate this multidimensional structure. In particular, he initially considers operators for multidimensional aggregate data which extend relatio...

Quadrature Estimates for Multidimensional Integrals

We prove estimates for the error in the most straightforward discrete approximation to the integral of a compactly supported function of n variables. The methods use Fourier analysis and interpolation theory, and also make contact with classical lattice point estimates. We also prove error estimates for the approximation of the integral over an interval by the trapezoidal rule and the midpoint ...

A Trace Formula for Multidimensional Schrödinger Operators

We prove multidimensional analogs of the trace formula obtained previously for one-dimensional Schrödinger operators. For example, let V be a continuous function on [0, 1] ⊂ R . For A ⊂ {1, . . . , ν}, let −∆A be the Laplace operator on [0, 1] with mixed Dirichlet-Neumann boundary conditions φ(x) = 0, xj = 0 or xj = 1 for j ∈ A, ∂φ ∂xj (x) = 0, xj = 0 or xj = 1 for j / ∈ A. Let |A| = number of ...