Orthonormal sampling functions

Rational Orthonormal Functions and Applications

Acknowledgement I am very grateful to Professor Ferenc Schipp for initiating me on the field of the approximation theory, for his advices and remarks without them this thesis would have been impossible. I am also indebted to the members of the Department of Numerical Analysis of the Eötvös Loránd University for their support during the years. I am especially grateful to Professor József Bokor i...

Modelling with Orthonormal Basis Functions

Strichartz Inequality for Orthonormal Functions

We prove a Strichartz inequality for a system of orthonormal functions, with an optimal behavior of the constant in the limit of a large number of functions. The estimate generalizes the usual Strichartz inequality, in the same fashion as the Lieb-Thirring inequality generalizes the Sobolev inequality. As an application, we consider the Schrödinger equation in a time-dependent potential and we ...

Ridge Functions and Orthonormal Ridgelets

Orthonormal ridgelets are a specialized set of angularly-integrated ridge functions which make up an orthonormal basis for L2(R). In this paper we explore the relationship between orthonormal ridgelets and true ridge functions r(x1 cos θ + x2 sin θ). We derive a formula giving the ridgelet coefficients of a ridge function in terms of the 1-D wavelet coefficients of the ridge profile r(t), and w...

System identification with generalized orthonormal basis functions

A least-squares identification method is studied that estimates a finite number of expansion coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized basis functions. The basis functions are orthogonal in 8$, and generalize the pulse, Laguerre and Kautz bases. One of their important properties is that, when chosen properly, ...