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...

Semi-nonparametric (SNP) models are models where only a part of the model is parametrized, and the non-specified part is an unknown function which is represented by an infinite series expansion. Therefore, SNP models are in essence models with infinitely many parameters. The theoretical foundation of series expansions of functions is Hilbert space theory, in particular the properties of Hilbert...

In this report we present a collection of results concerning two families of rational orthonormal functions, one on the unit circle, and another on the imaginary axis. We also describe in detail an interesting link between the two families. Special cases of these rational orthonormal functions include the Laguerre and Kautz orthonormal functions, as well as the orthonormal functions recently in...

It is well known that in the univariate case, up to an integer shift and possible sign change, there is no dyadic compactly supported symmetric orthonormal scaling function except for the Haar function. In this paper we are concerned with the construction of symmetric orthonormal scaling functions with dilation factor d = 4. Several examples of such scaling functions are provided in this paper....

Abstract In this paper, we consider some examples of set algebras $$ \mathcal{A} A on ℕ. If ℰ( ) is the simple functions , then ℒ ∗ α ( denotes ‖⋅‖ -closure ). Our aim to determine a complete orthonormal system for Hilbert space ∗2 in each regarded case. Here quotient modulo null-functions.