Tightness of bounds on rates of approximation by feedforward neural networks is investigated in a more general context of nonlinear approximation by variable-basis functions. Tight bounds on the worst case error in approximation by linear combinations of elements of an orthonormal variable basis are derived.

We consider the generalized Lorentz space L ;q dened via a continuous and concave function Fourier series of with respect to an unbounded orthonormal system. Some new Jackson-Nikol'skii type inequalities in this frame are stated, proved discussed. In particular, derived results generalize unify several well-known but also some applications pointed out.

where the component measure μ is Lebesgue supported on [t,t+1] for t∈ℚ∖{-1 2} and δ 0 Dirac at 0. We prove that ρ a spectral if only t∈1 2ℤ. In this case, L 2 (ρ) has unique orthonormal basis of form

In [RS], an explicit orthonormal basis of wavelets forL 2 (IR s ), s = 1; 2; 3, was constructed from a multiresolution approximation given by box splines. In other words, L 2 (IR s ) has the orthogonal decomposition

In this paper we give a constructive characterisation of ultraweakly continuous linear functionals on the space of bounded linear operators on a separable Hilbert space. Let H be a separable complex Hilbert space, with orthonormal basis (en)∞n=1, and B(H) the set of bounded linear operators on H . The weak operator norm associated with the orthonormal basis (en) is defined on B(H) by ‖T ‖w ≡ ∞ ...

In many areas of mathematics, orthonormal bases are a standard tool for representing vectors or operators. For certain problems, however, it is preferable to use an overcomplete, non-orthogonal set of vectors instead of an orthonormal basis, and thereby incorporate redundancy in the representation. Frames are overcomplete sets which are associated with redundant linear representations that have...

This paper considers the design of wavelet tight frames based on iterated oversampled lter banks. The greater design freedom available makes possible the construction of wavelets with a high degree of smoothness, in comparison with orthonormal wavelet bases. Grr obner bases are used to obtain the solutions to the nonlinear design equations. Following the dual-tree DWT of Kingsbury, one goal is ...

We propose alternative discriminant measures for selecting the best basis among a large collection of orthonormal bases for classification purposes. A generalization of the Local Discriminant Basis Algorithm of Saito and Coifman is constructed. The success of these new methods is evaluated and compared to earlier methods in experiments.

| This paper develops a general and very simple construction for complete orthonormal bases for system identiica-tion. This construction provides a unifying formulation of many previously studied orthonormal bases since the common FIR and recently popular Laguerre and two-parameter Kautz model structures are restrictive special cases of the construction presented here. However, in contrast to t...