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Shearlet tight frames have been extensively studied during the last years due to their optimal approximation properties of cartoon-like images and their unified treatment of the continuum and digital setting. However, these studies only…

Functional Analysis · Mathematics 2015-03-13 P. Kittipoom , G. Kutyniok , W. Lim

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…

Functional Analysis · Mathematics 2019-08-15 Sean Olphert , Stephen C. Power

We study variational obstacle avoidance problems on complete Riemannian manifolds and apply the results to the construction of piecewise smooth curves interpolating a set of knot points in systems with impulse effects. We derive the…

Optimization and Control · Mathematics 2021-08-31 Jacob R. Goodman , Leonardo J. Colombo

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…

Classical Analysis and ODEs · Mathematics 2018-04-10 Ilona Iglewska-Nowak

We consider the behavior of the nonlocal minimal surfaces in the vicinity of the boundary. By a series of detailed examples, we show that nonlocal minimal surfaces may stick at the boundary of the domain, even when the domain is smooth and…

Analysis of PDEs · Mathematics 2016-03-17 Serena Dipierro , Ovidiu Savin , Enrico Valdinoci

Given a compact interval $[a,b] \subset [0,\pi]$, we construct a parabolic self-map of the upper half-plane whose set of slopes is $[a,b]$. The nature of this construction is completely discrete and explicit: we explicitly construct a…

Complex Variables · Mathematics 2024-11-20 Manuel D. Contreras , Francisco J. Cruz-Zamorano , Luis Rodríguez-Piazza

The construction of needlet-type wavelets on sections of the spin line bundles over the sphere has been recently addressed in Geller and Marinucci (2008), and Geller et al. (2008,2009). Here we focus on an alternative proposal for needlets…

Classical Analysis and ODEs · Mathematics 2013-03-12 Daryl Geller , Domenico Marinucci

In applications that involve interactive curve and surface modeling, the intuitive manipulation of shapes is crucial. For instance, user interaction is facilitated if a geometrical object can be manipulated through control points that…

Functional Analysis · Mathematics 2017-10-11 Daniel Schmitter , Julien Fageot , Anaïs Badoual , Pablo Garcia-Amorena , Michael Unser

We present a preconditioning method for the multi-dimensional Helmholtz equation with smoothly varying coefficient. The method is based on a frame of functions, that approximately separates components associated with different singular…

Numerical Analysis · Mathematics 2010-10-25 Christiaan C. Stolk

In this work, we carry out structural and algorithmic studies of a problem of barrier forming: selecting theminimum number of straight line segments (barriers) that separate several sets of mutually disjoint objects in the plane. The…

Robotics · Computer Science 2022-02-25 Si Wei Feng , Jingjin Yu

We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…

Statistics Theory · Mathematics 2007-06-13 Anestis Antoniadis , Efstathios Paparoditis , Theofanis Sapatinas

Perfect reconstruction filter banks can be used to generate a variety of wavelet bases. Using IIR linear phase filters one can obtain symmetry properties for the wavelet and scaling functions. In this paper we describe all possible IIR…

Numerical Analysis · Mathematics 2011-12-23 Lucas Monzon

We use Daubechies' orthonormal compact wavelets as a variational basis for the $XY$ model in two and three dimensions. Assuming that the fluctuations of the wavelet coefficients are Gaussian and uncorrelated, minimization of the free energy…

High Energy Physics - Lattice · Physics 2009-10-22 C. Best , A. Schaefer

A set of orthogonal polynomials on the unit disk $B(0,1)$ known as Zernike polynomials are commonly used in the analysis and evaluation of optical systems. Here Zernike polynomials are used to construct wavelets for polynomial subspaces of…

Functional Analysis · Mathematics 2025-07-24 Somantika Datta , Kanti B. Datta

A wavelet-like model for distributions of objects in natural and man-made terrestrial environments is developed. The model is constructed in a self-similar fashion, with the sizes, amplitudes, and numbers of objects occurring at a constant…

Data Analysis, Statistics and Probability · Physics 2013-12-20 D. Keith Wilson , Chris L. Pettit , Sergey N. Vecherin

We study discrete solitons in zigzag discrete waveguide arrays with different types of linear mixing between nearest-neighbor and next-nearest-neighbor couplings. The waveguide array is constructed from two layers of one-dimensional (1D)…

Pattern Formation and Solitons · Physics 2020-04-14 Jinzhou Hu , Shulan Li , Zhaopin Chen , Jiantao Lu , Bin Liu , Yongyao Li

We report on existence and properties of discrete gap solitons in zigzag arrays of alternating waveguides with positive and negative refractive indices. Zigzag quasi-one-dimensional configuration of waveguide array introduces strong…

Pattern Formation and Solitons · Physics 2015-09-16 Alexander A. Dovgiy , Ilya S. Besedin

This work presents a framework for a-posteriori error-estimating algorithms for differential equations which combines the radii polynomial approach with Haar wavelets. By using Haar wavelets, we obtain recursive structures for the matrix…

Numerical Analysis · Mathematics 2023-05-01 Guilherme Nakassima , Marcio Gameiro

We give an equivariant version of Packer and Rieffel's theorem on sufficient conditions for the existence of orthonormal wavelets in projective multiresolution analyses. The scaling functions that generate a projective multiresolution…

Functional Analysis · Mathematics 2007-09-27 Kjetil Røysland

We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…

Numerical Analysis · Mathematics 2024-05-30 Daniel Potts , Laura Weidensager