Related papers: Bivariate Daubechies Scaling Functions (Wavelets)
The paper addresses the study and applications of a broad class of extended-real-valued functions, known as optimal value or marginal functions, which are frequently appeared in variational analysis, parametric optimization, and a variety…
We intend to derive the moment and exponential tail estimates for the so-called bivariate or more generally multivariate functional operations, not necessary to be linear or even multilinear. We will show also the strong or at last weak…
In the paper we design a Parseval wavelet frame with a compact support. The corresponding refinement mask uniformly approximates an arbitrary continuous periodic function $f$, $f(0)=1$, $|f(x)|^2+|f(x+\pi)|^2\le 1$. The refinable function…
We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…
Daubechies-type theorems for localization operators are established in the multi-variate setting, where Hagedorn wavepackets are identified as the proper substitute of the Hermite functions. The class of Reinhardt domains is shown to be the…
This paper discusses the generation of multivariate $C^\infty$ functions with compact small supports by subdivision schemes. Following the construction of such a univariate function, called \emph{Up-function}, by a non-stationary scheme…
An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our…
Research on refinable functions in wavelet theory is mostly focused to localized functions. However it is known, that polynomial functions are refinable, too. In our paper we investigate on conversions between refinement masks and…
We start by presenting a generalization of a discrete wave equation that is particularly satisfied by the entries of the matrix coefficients of the refinement equation corresponding to the multiresolution analysis of Alpert. The entries are…
In this paper we provide a complete and unifying characterization of compactly supported univariate scalar orthogonal wavelets and vector-valued or matrix-valued orthogonal multi-wavelets. This characterization is based on classical results…
This paper offers a new regard on compactly supported wavelets derived from FIR filters. Although being continuous wavelets, analytical formulation are lacking for such wavelets. Close approximations for daublets (Daubechies wavelets) and…
In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation…
A theory of higher rank multiresolution analysis is given in the setting of abelian multiscalings. This theory enables the construction, from a higher rank MRA, of finite wavelet sets whose multidilations have translates forming an…
Numerical optimization is used to construct new orthonormal compactly supported wavelets with Sobolev regularity exponent as high as possible among those mother wavelets with a fixed support length and a fixed number of vanishing moments.…
We tensorize the Faber spline system from [14] to prove sequence space isomorphisms for multivariate function spaces with higher mixed regularity. The respective basis coefficients are local linear combinations of discrete function values…
We study the scaling behavior of the fluctuations, as extracted through wavelet coefficients based on discrete wavelets. The analysis is carried out on a variety of physical data sets, as well as Gaussian white noise and binomial…
Adapting the recently developed randomized dyadic structures, we introduce the notion of spline function in geometrically doubling quasi-metric spaces. Such functions have interpolation and reproducing properties as the linear splines in…
A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces is derived. It allows one to represent a density into independent and interactive parts, the former being built as the product of revised…
The multiresolution analysis of Alpert is considered. Explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions. These entries are shown to solve generalized…
We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…