Related papers: An Interpolatory Estimate for the UMD-Valued Direc…
Main goal of this paper is to generalize Hadamard's real part theorem and invariant forms of Borel-Carath\'eodory's theorem from complex analysis to solutions of the Riesz system in the three-dimensional Euclidean space in the framework of…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
We propose the first deep learning solution to video frame inpainting, a challenging instance of the general video inpainting problem with applications in video editing, manipulation, and forensics. Our task is less ambiguous than frame…
Error estimation of difference operators on irregular nodes is discussed. We can obtain the similar estimates of the errors. However, the error estimate for the difference operators for the second derivatives becomes lower because of…
We consider the numerical evaluation of one dimensional projections of general multivariate stable densities introduced by Abdul-Hamid and Nolan (1998). In their approach higher order derivatives of one dimensional densities are used, which…
Analogous of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflection group. The $L^p$ boundedness of these operators is…
We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of solving ODEs in a verified way, i.e., with full control of…
Among their competitors, projection depth and its induced estimators are very favorable because they can enjoy very high breakdown point robustness without having to pay the price of low efficiency, meanwhile providing a promising…
This note is concerned with lower tail estimates for product measures. Some improved deviation inequalities are obtained for functions satisfying some regularity and monotonicity assumptions. The arguments are based on semigroup…
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 theoretically describe the optical computation of the divergence of a two-dimensional vector field, which is composed by the transverse electric field components of an incident light beam. The divergence is computed in reflection at…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
We establish sharp pointwise inequalities for the Riesz potential and its gradient in $\mathbb{R}^{n}$ and indicate their usefulness for potential analysis, moment theory and other applications.
We develop a theory of extrapolation for weights that satisfy a generalized reverse H\"older inequality in the scale of Orlicz spaces. This extends previous results by Auscher and Martell [2] on limited range extrapolation. As an…
Consider an Archimedean partially ordered vector space $X$ with generating cone (or, more generally, a pre-Riesz space $X$). Let $P$ be a linear projection on $X$ such that both $P$ and its complementary projection $I - P$ are positive; we…
The projection of sample measurements onto a reconstruction space represented by a basis on a regular grid is a powerful and simple approach to estimate a probability density function. In this paper, we focus on Riesz bases and propose a…
We present a slightly simpler proof of the multilinear refined Strichartz estimate, and prove a slightly more general linear refined Strichartz estimate. Our arguments seek to clarify the connection between these estimates, refined…
Inspired by a recent work of M. Nakasuji, O. Phuksuwan and Y. Yamasaki we combine interpolated multiple zeta values and Schur multiple zeta values into one object, which we call interpolated Schur multiple zeta values. Our main result will…
In this present paper, I propose a derivation of unified interpolation and extrapolation function that predicts new values inside and outside the given range by expanding direct Taylor series on the middle point of given data set.…
New results about Poisson-Dirichlet point processes and Derrida-Ruelle cascades allow us to express Guerra's interpolation entirely in the language of Derrida-Ruelle cascades and to streamline Guerra's computations. Moreover, our approach…