Related papers: Multiresolution in the Bergman space
The Patterson-Sullivan construction is proved almost surely to recover a Bergman function from its values on a random discrete subset sampled with the determinantal point process induced by the Bergman kernel on the unit ball $\mathbb{D}_d$…
We identify multiresolution subspaces giving rise via Hankel transforms to Bessel functions. They emerge as orthogonal systems derived from geometric Hilbert-space considerations, the same way the wavelet functions from a multiresolution…
We identify multiresolution subspaces giving rise via Hankel transforms to Bessel functions. They emerge as orthogonal systems derived from geometric Hilbert-space considerations, the same way the wavelet functions from a multiresolution…
We present a construction of a wavelet-type orthonormal basis for the space of radial $L^2$-functions in $\R^3$ via the concept of a radial multiresolution analysis. The elements of the basis are obtained from a single radial wavelet by…
We present the applications of variation -- wavelet analysis to polynomial/rational approximations for orbital motion in transverse plane for a single particle in a circular magnetic lattice in case when we take into account multipolar…
A multiresolution analysis for a Hilbert space realizes the Hilbert space as the direct limit of an increasing sequence of closed subspaces. In a previous paper, we showed how, conversely, direct limits could be used to construct Hilbert…
Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…
This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…
We find sufficient conditions for a discrete sequence to be interpolating or sampling for certain generalized Bergman spaces on open Riemann surfaces. As in previous work of Bendtsson, Ortega-Cerda, Seip, Wallsten and others, our conditions…
We introduce \`a la Vasilevski the weighted poly-Bergman spaces in the unit disc and provide concrete orthonormal basis and give close expression of their reproducing kernel. The main tool in the description if these spaces is the so-called…
We construct a multiresolution theory for spaces bigger then L^2(R). For a good choice of the dilation and translation operators on these larger spaces, it is possible to build singly generated wavelet bases, thus obtaining examples of…
A generalization of Mallat's classic theory of multiresolution analysis based on the theory of spectral pairs was considered by Gabardo and Nashed (J. Funct. Anal. 158, 209-241, 1998). In this article, we introduce the notion of…
In the present paper, multiscale systems of polynomial wavelets on an n-dimensional sphere are constructed. Scaling functions and wavelets are investigated,and their reproducing and localization properties and positive definiteness are…
Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static…
Modeling time-harmonic Maxwell problems in heterogeneous media presents significant mathematical and computational challenges. Due to the inherent non-elliptic structure and non-coercive nature of Maxwell equations, conventional methods…
For $\alpha>-1$ and $0<p<\infty$, we study weighted Bergman spaces $\mathcal B^p_\alpha$ of harmonic functions on the real hyperbolic ball and obtain an atomic decomposition of these spaces in terms of reproducing kernels. We show that an…
We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies…
Bayes spaces were initially designed to provide a geometric framework for the modeling and analysis of distributional data. It has recently come to light that this methodology can be exploited to provide an orthogonal decomposition of…