It is a well known fact that any orthonormal basis in L 2 can produce a \random density". If fng is an orthonormal basis and fang is a sequence of random variables such that a 2 n = 1 a.s., then f(x) = jann(x)j 2 is a random density. In this note we deene a random density via orthogonal bases of wavelets and explore some of its basic properties.

Let {4>„{dfi)} be a system of orthonormal polynomials on the unit circle with respect to d/i and {y/„,m(dß)} be a system of orthonormal polynomials on the unit circle with respect to the varying measures dß/\wn(z)\2, z = e'e , where {w„(z)} is a sequence of polynomials, degw« = n , whose zeros w„ i, ... , wn,n lie in \z\ < 1 The asymptotic behavior of the ratio of the two systems on and outside...

The energy-momentum for a gravitating system can be considered by the tetard teleparalle gauge current in orthonormal frames. Whereas the Einstein pseudotensor used holonomic frames. Tetrad expression itself gives a better result for gravitational energy than Einstein’s. Inspired by an idea of Deser, we found a gravitational energy expression which enjoys the positive energy property by combini...

Vector fitting is widely accepted as a robust macromodelling tool for efficient frequency domain identification of passive components. The orthonormal vector fitting technique is introduced, which improves the numerical stability of the method, by using orthonormal rational functions. This leads to better conditioned equations, reduces the numerical sensitivity to the choice of starting poles s...

Abstract We present a dimension-incremental algorithm for the nonlinear approximation of high-dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to detect suitable truncation basis expansion function, where corresponding support assumed be unknown. method based on point evaluations considered function and adaptively builds index set such that approximately larg...

This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalized orthonormal basis functions. The paper is separated in two parts. The first part of the paper approached issues related with linear models and models with uncertain parameters. Now, the mathematical foundations as well as their advantages and ...

The method of Dubuc and Deslauriers on symmetric interpolatory subdivision is extended to study the relationship between interpolation processes and wavelet construction. Refinable and interpolatory functions are constructed in stages from B-splines. Their method constructs the filter sequence (its Laurent polynomial) of the interpolatory function as a product of Laurent polynomials. This provi...

We address the problem of restoring, while preserving possible discontinuities, fields of noisy orthonormal vector sets, taking the orthonormal constraints explicitly into account. We develop a variational solution for the general case where each image feature may correspond to multiple n-D orthogonal vectors of unit norms. We first formulate the problem in a new variational framework, where di...