Related papers: Matched wavelets for equidistant points
In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a…
We propose a novel theoretical framework for barycentric interpolation, using concepts recently developed in mathematical physics. Generalized barycentric coordinates are defined similarly to Shepard's method, using positive geometries -…
Increasingly complex data analysis tasks motivate the study of the dependency of distributions of multivariate continuous random variables on scalar or vector predictors. Statistical regression models for distributional responses so far…
Wavelet systems on the generalized Vilenkin groups are considered. An algorithmic method for the construction of orthogonal wavelet bases is presented. These bases consist of compactly supported test functions (i.e. functions whose Fourier…
In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
In pursuit of a minimal basis for systems with non-ideal bond angles, in this work we try to pinpoint the exact orientation of the major overlapping orbitals along the nearest neighbouring coordination segments in a given system such that…
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…
Kostelecky and Mewes have recently shown that sensitive constraints can be placed on some aspects of Lorentz symmetry violation using certain astronomical data on high-redshift sources. Here, I introduce that data in its astronomical…
This note is intended as a brief introduction to the theory and practice of perfectly matched layer (PML) absorbing boundaries for wave equations, originally developed for MIT courses 18.369 and 18.336. It focuses on the complex…
In this paper, we obtain two interpolation theorems on convex-set valued Lebesgue spaces, which generalize the Marcinkiewicz interpolation theorem and Riesz-Thorin interpolation theorem on classical Lebesgue spaces, respectively. As…
We prove intertwining relations by twisted gradients for Markov semi-groups. These relations are applied to Brascamp-Lieb type inequalities and spectral gap results. It generalizes the results of [1] from the Euclidean space to Riemannian…
Full polarimetric radio interferometric calibration is performed by estimating 2 by 2 Jones matrices representing instrumental and propagation effects. The solutions obtained in this way differ from the true solutions by a 2 by 2 unitary…
Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples, which was introduced in \cite{DHSS}. In this paper, we shall construct Riesz wavelet associated with dual pseudo splines. Furthermore, we…
An interpolation problem related to the elliptic Painlev\'e equation is formulated and solved. A simple form of the elliptic Painlev\'e equation and the Lax pair are obtained. Explicit determinant formulae of special solutions are also…
In this paper we introduce a new family of wavelets, named Chebyshev wavelets, which are derived from conventional first and second kind Chebyshev polynomials. Properties of Chebyshev filter banks are investigated, including orthogonality…
Single-wavelength interferometry achieves high resolution for smooth surfaces but struggles with rough, industrially relevant ones due to limited unambiguous measuring range and speckle effects. Multi-wavelength interferometry addresses…
This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes…
Partial Differential Equations (PDEs) models for wave propagation in inhomogeneous media are relevant for many applications. We will discuss numerical methods tailored for tackling problems governed by these variable-coefficient PDEs.…
Implicit particle filters for data assimilation generate high-probability samples by representing each particle location as a separate function of a common reference variable. This representation requires that a certain underdetermined…