Related papers: Continuous Shearlet Tight Frames
This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a…
This paper proposes a tractable family of remainder-form mixed-monotone decomposition functions that are useful for over-approximating the image set of nonlinear mappings in reachability and estimation problems. Our approach applies to a…
The realization space of geometric constraint systems is given by the vanishing locus of polynomials corresponding to natural geometric constraints. Such geometric constraint systems arise in many real-world scenarios such as structural…
We express characteristic numbers of compact hyperk\"ahler manifolds in graph-theoretical form, considering them as a special case of the curvature invariants introduced by Rozansky and Witten. The appropriate graphs are generated by…
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic and fulfill the polyconvexity condition, which implies…
This paper provides maximal function characterizations of anisotropic Triebel-Lizorkin spaces associated to general expansive matrices for the full range of parameters $p \in (0,\infty)$, $q \in (0,\infty]$ and $\alpha \in \mathbb{R}$. The…
We introduce the notion of rigidity for automorphic representations of groups over global function fields. We construct the Langlands parameters of rigid automorphic representations explicitly as local systems over open curves. We expect…
A construction of conservation laws for chiral models (generalized sigma-models on a two-dimensional space-time continuum using differential forms is extended in such a way that it also comprises corresponding discrete versions. This is…
Textures in images can often be well modeled using self-similar processes while they may at the same time display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific…
We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as…
We show that for any uniformly elliptic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term one can find an approximating equation which has a unique continuous and having the second…
In the paper we design a Parseval wavelet frame with a compact support and many vanishing moments. The corresponding refinement mask approximates an arbitrary continuous periodic function $f$, $f(0)=1$. The refinable function has stable…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
Let $\mathcal{D}$ be the dictionary of Gaussian mixtures: the functions created by affine change of variables of a single Gaussian in $n$ dimensions. $\mathcal{D}$ is used pervasively in scientific applications to a degree that…
We establish the existence of `time quasilattices' as stable trajectories in dissipative dynamical systems. These tilings of the time axis, with two unit cells of different durations, can be generated as cuts through a periodic lattice…
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…
We apply thermodynamic formalism to a generalized horseshoe map. We prove that a tailored anisotropic Banach space with weighted norms yields a spectral gap for the transfer operator, implying the existence of a unique physical measure.…
We provide the construction of a set of square matrices whose translates and rotates provide a Parseval frame that is optimal for approximating a given dataset of images. Our approach is based on abstract harmonic analysis techniques.…
Recently, continuous representation methods emerge as novel paradigms that characterize the intrinsic structures of real-world data through function representations that map positional coordinates to their corresponding values in the…