ﻻ يوجد ملخص باللغة العربية
In this paper we develop the calculus of pseudo-differential operators corresponding to the quantizations of the form $$ Au(x)=int_{mathbb{R}^n}int_{mathbb{R}^n}e^{i(x-y)cdotxi}sigma(x+tau(y-x),xi)u(y)dydxi, $$ where $tau:mathbb{R}^ntomathbb{R}^n$ is a general function. In particular, for the linear choices $tau(x)=0$, $tau(x)=x$, and $tau(x)=frac{x}{2}$ this covers the well-known Kohn-Nirenberg, anti-Kohn-Nirenberg, and Weyl quantizations, respectively. Quantizations of such type appear naturally in the analysis on nilpotent Lie groups for polynomial functions $tau$ and here we investigate the corresponding calculus in the model case of $mathbb{R}^n$. We also give examples of nonlinear $tau$ appearing on the polarised and non-polarised Heisenberg groups, inspired by the recent joint work with Marius Mantoiu.
This paper is devoted to wavelet analysis on adele ring $bA$ and the theory of pseudo-differential operators. We develop the technique which gives the possibility to generalize finite-dimensional results of wavelet analysis to the case of adeles $bA$
We consider a smooth hyper-surface Z of a closed Riemannian manifold X. Let P be the Poisson operator associating to a smooth function on Z its harmonic extension on XZ. If A is a pseudo-differential operator on X of degree <3, we prove that B=P^* A
In this article, we begin a systematic study of the boundedness and the nuclearity properties of multilinear periodic pseudo-differential operators and multilinear discrete pseudo-differential operators on $L^p$-spaces. First, we prove analogues of k
Infinite order differential operators appear in different fields of Mathematics and Physics and in the last decades they turned out to be of fundamental importance in the study of the evolution of superoscillations as initial datum for Schrodinger eq
Given a compact (Hausdorff) group $G$ and a closed subgroup $H$ of $G,$ in this paper we present symbolic criteria for pseudo-differential operators on compact homogeneous space $G/H$ characterizing the Schatten-von Neumann classes $S_r(L^2(G/H))$ fo