Let M be a space of weakly*-measurable functions F : ? B(H) on measure (?,?,?), for which the function F*F is Gel'fand integrable and integral d? nuclear operator Hilbert H. We show that H*-module contains an orthonormal basis.

Nonlinear block-oriented systems, including the Hammerstein, Wiener and feedbacknonlinear systems have attracted considerable research interest both from the industrial and academic environments (Bai, 1998), (Greblicki, 1989), (Latawiec, 2004), (Latawiec et al., 2003), (Latawiec et al., 2004), (Pearson & Pottman, 2000). It is well known that orthonormal basis functions (OBF) (Bokor et al., 1999...

Nonlinear adaptive ltering has witnessed an explosion of interest in recent years. This progress report describes the achievements to date of the EPSRC funded research program to investigate orthonormal functions for nonlinear signal processing. The report introduces a structure based upon the multi{dimensional Fourier series which can be applied to nonlinear system identi-cation, channel equal...

In this paper we calibrate the stationary Gaussian Musiela model to time series of market data using the Karhunen-Loeve expansion in order to get an ortonormal basis (classically known as EOF, empirical orthonormal functions) in a separable Hilbert space. The basis found is optimal for representing the covariance of the invariant measure of the forward rates’ process.

We propose alternative discriminant measures for selecting the best basis among a large collection of orthonormal bases for classi cation 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.

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.

Introduction The question of positivity of curvature on bundles arose in the middle 60's with O'Neills theorem [O], according to which riemannian submersions increase the sectional curvature. In the early 70's Cheeger and Gromoll in their notable paper [C-G], showed that if an open manifold has a complete riemannian metric with non-negative sectional curvature then it is the total space of a ve...

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 this paper, we show how to construct an orthonormal basis from Riesz by assuming that the fractional translates of a single function in core subspace multiresolution analysis form instead basis. definition analysis, intersection triviality condition follows other conditions. Furthermore, union density also under assumption Fourier transform scaling is continuous at 0. At culmination, provide...

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