A framework for coherent pattern extraction and prediction of observables measure-preserving, ergodic dynamical systems with both atomic continuous spectral components is developed. This based on an approximation the generator system by a compact operator Wτ reproducing kernel Hilbert space (RKHS). The skew-adjoint, thus can be represented projection-valued measure, discrete compactness, associ...

In this paper we show that every g-frame for a Hilbert space H can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. We also show that every g-frame can be written as a sum of two tight g-frames with g-frame bounds one or a sum of a g-orthonormal basis and a g-Riesz basis for H . We further give necessary and sufficient conditions on g-Besse...

We construct a monomial basis of the positive part U of the quantized enveloping algebra associated to a finite–dimensional simple Lie algebra. As an application we give a simple proof of the existence and uniqueness of the canonical basis of U. 0. Introduction In [L1], Lusztig showed that the positive part U of the quantized enveloping algebra associated to a finite–dimensional simple Lie alge...

For an arbitrary full rank lattice Λ in R and a function g ∈ L(R) the Gabor (or Weyl-Heisenberg) system is G(Λ, g) := {eg(x − κ) ̨ ̨ (κ, `) ∈ Λ}. It is well-known that a necessary condition for G(Λ, g) to be an orthonormal basis for L(R) is that the density of Λ has D(Λ) = 1. However, except for symplectic lattices it remains an unsolved question whether D(Λ) = 1 is sufficient for the existence o...

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.