The homogeneous approximation property (HAP) is useful in practice since it means that the number of building blocks involved in a reconstruction of f up to some error is essentially invariant under time-scale shifts. In this paper, we prove the HAP for a large class of wavelet frames which are generated with arbitrary time-scale shifts and wavelet functions satisfying moderate decaying conditi...

We study the weak bounded approximation property (weak BAP) of pairs and show that each of the spaces c0 and `1 has a subspace having the approximation property but failing the weak BAP.

The central point of our proof is an observation that the proof of the same property for free groups due to Haagerup [2] transfers directly to this more general situation. A discrete group Γ satisfies property (RD) (Rapid Decay) with respect to a length function l on Γ if the operator norm of any element of the group ring can be uniformly majorised by a Sobolev norm determined by l. In detail, ...

Using the power series method, we solve the inhomogeneous linear first order differential equation y′(x) + λ(x− μ)y(x) = ∞ X

This paper examines the fuzzy system for function approximation in a macroscopic level. The rules of a fuzzy function approximation system are expressed in the form of polynomials such that each rule forms a local approximator. We show that this kind of fuzzy function approximation is equivalent to piecewise polynomial interpolation between turning points when normalized fuzzy function membersh...

An irregular wavelet frame has the form W(ψ,Λ) = {aψ( a − b)}(a,b)∈Λ, where ψ ∈ L (R) and Λ is an arbitrary sequence of points in the affine group A = R ×R. Such irregular wavelet frames are poorly understood, yet they arise naturally, e.g., from sampling theory or the inevitability of perturbations. This paper proves that irregular wavelet frames satisfy a Homogeneous Approximation Property, w...