In this paper we give a sufficient condition of the existence of W-approximation representations. We also introduce the notion of property (W). As an application to the existence of W -approximation representations we give a relationship among the finitistic dimension conjecture, the Auslander-Reiten conjecture and property (W).

All normalized totally positive bases satisfy the progressive iterative approximation property. The normalized B-basis has optimal shape preserving properties and we prove that it satisfies the progressive iterative approximation property with the fastest convergence rates. A similar result for tensor product surfaces is also derived. © 2006 Elsevier B.V. All rights reserved.

In this paper we give a sufficient condition of the existence of W-approximation presentations. We also introduce property (W). As an application of the existence of W-approximation presentations we give a connection between the finitistic dimension conjecture, the Auslander-Reiten conjecture and property (W).

We point out that an approximation property of Gaussian functions, derived in a recent work, is a direct corollary to the work of Wiener on the closure of translations in L1 and L2. This observation not only simplifies the proof of the approximation property, but also renders the result applicable, in a more general setting, to other functions (not necessarily Gaussian).

Restricted non-linear approximation is a type of N-term approximation where a measure ν on the index set (rather than the counting measure) is used to control the number of terms in the approximation. We show that embeddings for restricted non-linear approximation spaces in terms of weighted Lorentz sequence spaces are equivalent to Jackson and Bernstein type inequalities, and also to the upper...

We define a perturbative approximation for the solution of Lindblad master equations with time-dependent generators that satisfies the fundamental property of complete positivity, as essential for quantum simulations and optimal control. With explicit examples we show that ensuring this property substantially improves the accuracy of the perturbative approximation.

Let R be a commutative noetherian local ring with completion b R. When R has the approximation property, we prove an approximation result for complexes with finitely generated homology. This is used to investigate descent of semidualizing complexes from b R to R. We show that, if R has the approximation property, then there is a bijective correspondence between semidualizing b R-complexes and s...