Related papers: Local approximation using Hermite functions

The Hermite functions are an orthonormalbasis of the space of square integrable functions with favourable approximation properties. Allowing for a flexible localization in position and momentum, the Hagedorn wavepackets generalize the…

We study approximation properties of linear sampling operators in the spaces $L_p$ for $1\le p<\infty$. By means of the Steklov averages, we introduce a new measure of smoothness that simultaneously contains information on the smoothness of…

The localized eigenstates of the Harper equation exhibit universal self-similar fluctuations once the exponentially decaying part of a wave function is factorized out. For a fixed quantum state, we show that the whole localized phase is…

This paper proposes a local representation for Empirical Likelihood (EL). EL admits the classical local linear quadratic representation by its likelihood ratio property. A local estimator is derived by using the new representation.…

In this paper we present a comprehensive treatment of function spaces with logarithmic smoothness (Besov, Sobolev, Triebel-Lizorkin). We establish the following results: Sharp embeddings between the Besov spaces defined by differences and…

Using normalized Hermite functions, we construct bases in the space of square integrable functions on the unit circle ($L^2(\mathcal C)$) and in $l_2(\mathbb Z)$, which are related to each other by means of the Fourier transform and the…

We show that any function can be locally approximated by solutions of prescribed linear equations of nonlocal type. In particular, we show that every function is locally $s$-caloric, up to a small error. The case of non-elliptic and…

We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Two general approaches to this problem have been developed:…

We consider models for multivariate point processes where the intensity is given nonparametrically in terms of functions in a reproducing kernel Hilbert space. The likelihood function involves a time integral and is consequently not given…

In this paper, we propose a new construction for the Mexican hat wavelets on shapes with applications to partial shape matching. Our approach takes its main inspiration from the well-established methodology of diffusion wavelets. This novel…

We provide a general treatment of perturbations of a class of functionals modeled on convolution energies with integrable kernel which approximate the $p$-th norm of the gradient as the kernel is scaled by letting a small parameter…

In generalized Lebesgue spaces L^{p(.)} with variable exponent p(.) defined on the real axis, we obtain several inequalities of approximation by integral functions of finite degree. Approximation properties of Bernstein singular integrals…

An approximation, in the sense of $\Gamma$-convergence and in any dimension $d\geq1$, of Griffith-type functionals, with $p-$growth ($p>1$) in the symmetrized gradient, is provided by means of a sequence of non-local integral functionals…

In this note, we study maximizers for Fourier extension inequalities on the sphere. We prove that constant functions are local maximizers for the $L^p(\mathbb{S}^{d-1})$ to $L^p(\mathbb{R}^d)$ Fourier extension estimates in the same range…

We study the elliptic maximal functions defined by averages over ellipses and rotated ellipses which are multi-parametric variants of the circular maximal function. We prove that those maximal functions are bounded on $L^p$ for some $p\neq…

We introduce new moduli of smoothness for functions $f\in L_p[-1,1]\cap C^{r-1}(-1,1)$, $1\le p\le\infty$, $r\ge1$, that have an $(r-1)$st locally absolutely continuous derivative in $(-1,1)$, and such that $\varphi^rf^{(r)}$ is in…

Let $D\subset\mathbb C^n$ be a bounded, strongly Levi-pseudoconvex domain with minimally smooth boundary. We prove $L^p(D)$-regularity for the Bergman projection $B$, and for the operator $|B|$ whose kernel is the absolute value of the…

We prove that any given function can be smoothly approximated by functions lying in the kernel of a linear operator involving at least one fractional component. The setting in which we work is very general, since it takes into account…

Let a continuous random process $X$ defined on $[0,1]$ be $(m+\beta)$-smooth, $0\le m, 0<\beta\le 1$, in quadratic mean for all $t>0$ and have an isolated singularity point at $t=0$. In addition, let $X$ be locally like a $m$-fold…

We establish sharp $L^p$ integral mean estimates for $(\alpha,\beta)$-harmonic functions on the unit disk. Explicit bounds for the functions and their partial derivatives are obtained in terms of boundary data, by means of the associated…