Related papers: Symmetries in projective multiresolution analyses
Parseval and equal-norm frames play a fundamental role in frame theory and signal processing. In this work, we prove non-asymptotic concentration bounds showing that random equal-norm frames are nearly Parseval with high probability, and…
Let X be a complex, rationally connected, projective manifold. We show that X admits a modification X' that contains a quasi-line, ie a smooth rational curve whose normal bundle is a direct sum of copies of O_{P^1}(1). For manifolds…
This paper concerns upper estimates of the projectional coderivative of implicit mappings and corresponding applications on analyzing the relative Lipschitz-like property. Under different constraint qualifications, we provide upper…
Performing both right and left multiplication operations using general regular matrix polynomials, which need not be monic and may possess leading coefficients of arbitrary rank, on a rectangular matrix of measures associated with mixed…
Characterization results for equality cases and for rigidity of equality cases in Steiner's perimeter inequality are presented. (By rigidity, we mean the situation when all equality cases are vertical translations of the Steiner's symmetral…
For a discrete group $\Gamma$ satisfying some finiteness conditions we give a Bredon projective resolution of the trivial module in terms of projective covers of the chain complex associated to certain posets of subgroups. We use this to…
Toric ideals to hierarchical models are invariant under the action of a product of symmetric groups. Taking the number of factors, say m, into account, we introduce and study invariant filtrations and their equivariant Hilbert series. We…
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…
The theory of orthonormal wavelet bases is a useful tool in multifractal analysis, as it provides a characterization of the different exponents of pointwise regularities (H{\"o}lder, p-exponent, lacunarity, oscillation, etc.). However, for…
In a normed space setting, this paper studies the conditions under which the projected solutions to a quasi equilibrium problem with non-self constraint map exist. Our approach is based on an iterative algorithm which gives rise to a…
In this note we announce that under general hypotheses, wavelet-type expansions (of functions in $L^p,\ 1\leq p \leq \infty$, in one or more dimensions) converge pointwise almost everywhere, and identify the Lebesgue set of a function as a…
Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parametrizing isomorphism classes of geometric objects (vector bundles, polarized…
In this paper we describe a 1-dimensional variational approach to the analytical construction of equivariant biharmonic maps. Our goal is to provide a direct method which enables analysts to compute directly the analytical conditions which…
This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…
We study skew-orthogonal polynomials with respect to the weight function $\exp[-2V(x)]$, with $V(x)=\sum_{K=1}^{2d}(u_{K}/{K})x^{K}$, $u_{2d} > 0$, $d > 0$. A finite subsequence of such skew-orthogonal polynomials arising in the study of…
Motivated by potential applications in multiplexing and by recent results on Gabor analysis with Hermite windows due to Gr\"{o}chenig and Lyubarskii, we investigate vector-valued wavelet transforms and vector-valued wavelet frames, which…
We provide explicit criteria for wavelets to give rise to frames and atomic decompositions in ${\rm L}^2(\mathbb{R}^d)$, but also in more general Banach function spaces. We consider wavelet systems that arise by translating and dilating the…
Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics…
We show that if an open cover of a finite dimensional space is equivariant with respect to some finite group action on the space then there is an equivariant refinement of bounded dimension. This will generalize some constructions of…
(Bi)orthogonal (multi)wavelets on the real line have been extensively studied and employed in applications with success. A lot of problems in applications are defined on bounded intervals or domains. Therefore, it is important in both…