Related papers: Existence of Uncertainty Minimizers for the Contin…
Larson's problem asks ``Must the support of the Fourier transform of a wavelet contain a wavelet set?". We give an affirmative answer to a non-measurable variant of this question by proving that the Fourier transform of a wavelet must…
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet…
Like the continous shearlet transform and their relatives, discrete transformations based on the interplay between several filterbanks with anisotropic dilations provide a high potential to recover directed features in two and more…
The optimal wavelet basis is used to develop quantitative, experimentally applicable criteria for self-organization. The choice of the optimal wavelet is based on the model of self-organization in the wavelet tree. The framework of the…
In the paper, asymptotic behavior of the uncertainty product for a family of zonal spherical wavelets is computed. The family contains the most popular wavelets, such as Gauss-Weierstrass, Abel-Poisson and Poisson wavelets and Mexican…
Objective detection of specific patterns in statistical distributions, like groupings or gaps or abrupt transitions between different subsets, is a task with a rich range of applications in astronomy: Milky Way stellar population analysis,…
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these…
Recent empirical work in the field of 'weak measurements' has yielded novel ways of more directly accessing and exploring the quantum wavefunction. Measuring either position or momentum for a photon in a 'weak' manner yields a wide range of…
Surface-consistent deconvolution is a standard processing technique in land data to uniformize the wavelet across all sources and receivers. The required wavelet estimation step is generally done in the homomorphic domain since this is a…
We establish lower semicontinuity results for perimeter functionals with measure data on $\mathbb{R}^n$ and deduce the existence of minimizers to these functionals with Dirichlet boundary conditions, obstacles, or volume-constraints. In…
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
We investigate the existence of subinvariant metric functionals for commuting families of nonexpansive mappings in noncompact subsets of Banach spaces. Our findings underscore the practicality of metric functionals when searching for fixed…
A cornerstone of current-density functional theory (CDFT) in its paramagnetic formulation is proven. After a brief outline of the mathematical structure of CDFT, the lower semi-continuity and expectation valuedness of the CDFT…
Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going efforts seek to better…
In this article, we derive conditions for the existence of solutions to state-constrained continuity inclusions in Wasserstein spaces whose right-hand sides may be discontinuous in time. These latter are based on a fine investigation of the…
Multiplicative cascades are often used to represent the structure of multiscaling variables in many physical systems, specially turbulent flows. In processes of this kind, these variables can be understood as the result of a successive…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider the applications of discrete wavelet analysis…
The purpose of this article is to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform (QFT). We study some fundamental properties of this extension such as scaling, translation,…
In the literature, necessary and sufficient conditions in terms of variational inequalities are introduced to characterize minimizers of convex set valued functions with values in a conlinear space. Similar results are proved for a weaker…