Related papers: Decay properties of Riesz transforms and steerable…
Upon decreasing the Reynolds number, plane Couette flow first forms alternately turbulent and laminar oblique bands out of featureless turbulence below some upper threshold R_t. These bands exist down to a global stability threshold R_g…
In this paper we study the Riesz transform on complete and connected Riemannian manifolds $M$ with a certain spectral gap in the $L^2$ spectrum of the Laplacian. We show that on such manifolds the Riesz transform is $L^p$ bounded for all $p…
In this paper, we present the concept of continuous biframes in a Hilbert space. We examine the essential properties of biframes with an emphasis on the biframe operator. Moreover, we introduce a new type of Riesz bases, referred to as…
We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact transform on the radial half-line using damped Laguerre…
We consider the Cauchy problem for incompressible viscoelastic fluids in the whole space $\mathbb{R}^d$ ($d=2,3$). By introducing a new decomposition via Helmholtz's projections, we first provide an alternative proof on the existence of…
Given a closed submanifold, or a compact regular domain, in euclidean space, we consider the Riesz energy defined as the double integral of some power of the distance between pairs of points. When this integral diverges, we compare two…
A traditional wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a system of unitary operators defined in terms of translation and dilation operations. A Coxeter/fractal-surface…
We present a systematic study of Riesz measures and their natural exponential families of Wishart laws on a homogeneous cone. We compute explicitly the inverse of the mean map and the variance function of a Wishart exponential family.
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…
It is challenging for full-waveform inversion to determine geologically informative models from field data. An inaccurate wavelet can make it more complicated. We develop a novel misfit function, entitled deconvolutional double-difference…
We consider Riesz transforms of any order associated to an Ornstein--Uhlenbeck operator $\mathcal L$, with covariance $Q$ given by a real, symmetric and positive definite matrix, and with drift $B$ given by a real matrix whose eigenvalues…
We study the properties of Modified Riemann extensions evolving under Ricci flow. We obtain the necessary and sufficient condition for modified Riemann extension under Ricci flow to stay as modified Riemann extension. We also discuss the…
We consider the optimization problem with a generally quadratic matrix constraint of the form $X^TAX = J$, where $A$ is a given nonsingular, symmetric $n\times n$ matrix and $J$ is a given $k\times k$ symmetric matrix, with $k\leq n$,…
We consider the damped wave semigroup on the tadpole graph ${\mathcal R}$. We first give a meticulous spectral analysis, followed by a judicious decomposition of the resolvent's kernel. As a consequence, and by showing that the generalized…
In this paper we introduce concepts of disjoint, strongly disjoint and weakly disjoint continuous $g$-frames in Hilbert spaces and we get some equivalent conditions to these notions. We also construct a continuous g-frame by disjoint…
Despite their self-reconstruction properties in heterogeneous media, Bessel beams are known to degenerate when they are refracted from an isotropic to an anisotropic medium. In this paper, we study the converse situation wherein an…
The Riesz transform of $u$ : $\mathcal{S}(\mathbb{R}^n) \rightarrow \mathcal{S'}(\mathbb{R}^n)$ is defined as a convolution by a singular kernel, and can be conveniently expressed using the Fourier Transform and a simple multiplier. We…
In this paper, we study $L^p$-boundedness ($1<p\leq 2$) of the covariant Riesz transform on differential forms for a class of non-compact weighted Riemannian manifolds without assuming conditions on derivatives of curvature. We present in…
We introduce a natural definition of Riesz measures and Wishart laws associated to an $\Omega$-positive (virtual) quadratic map, where $\Omega \subset \real^n$ is a regular open convex cone. We give a general formula for moments of the…
Sub-terahertz (Sub-THz) waves possess exceptional attributes, capable of penetrating non-metallic and non-polarized materials while ensuring bio-safety. However, their practicality in imaging is marred by the emergence of troublesome…