Orthogonal expansions of averaged functions

Quasi-orthogonal expansions for functions in BMO

For {φ_n(x)}, x ε [0,1] an orthonormalsystem of uniformly bounded functions, ||φ_n||_{∞}≤ M

Computing Derivatives of Noisy Signals Using Orthogonal Functions Expansions

In many applications noisy signals are measured. These signals has to be filtered and, sometimes, their derivative have to be computed. In this paper a method for filtering the signals and computing the derivatives is presented. This method is based on expansion onto transformed Legender polynomials. Numerical examples demonstrates the efficacy of the method as well as the theoretical estimates.

Combinatorial Orthogonal Expansions

so that amn is non-negative. In this paper we give in Theorem 1 and Theorem 2 explicit formulas for anm as a polynomial in the α ′ js, β ′ js and the γ ′ js, which give these theorems. The idea is to represent amn as a generating function of paths, whose weights are products of differences. Monotonicity hypotheses on the coefficients force the weights to be individually positive, these are the ...

On expansions in orthogonal polynomials

A recently introduced fast algorithm for the computation of the first N terms in an expansion of an analytic function into ultraspherical polynomials consists of three steps: Firstly, each expansion coefficient is represented as a linear combination of derivatives; secondly, it is represented, using the Cauchy integral formula, as a contour integral of the function multiplied by a kernel; final...

Summability of orthogonal expansions of several variables