Related papers: Exponential laws for weighted function spaces and …

Motivated by coarse geometry and the classical role of Roe algebras as large-scale invariants of proper metric spaces, we show that proper quantum metric spaces as introduced by Latr\'emoli\`ere are noncommutative coarse spaces. This…

Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…

We prove that the additive group $(E^\ast,\tau_k(E))$ of an $\mathscr{L}_\infty$-Banach space $E$, with the topology $\tau_k(E)$ of uniform convergence on compact subsets of $E$, is topologically isomorphic to a subgroup of the unitary…

E. Noether's general analysis of conservation laws has to be completed in a Lagrangian theory with local gauge invariance. Bulk charges are replaced by fluxes of superpotentials. Gauge invariant bulk charges may subsist when distinguished…

We generalize the Bernstein-Walsh-Siciak theorem on polynomial approximation in $\mathbb{C}^n$ to the case where the polynomial ring $\mathcal{P}(\mathbb{C}^n)$ is replaced by a subring $\mathcal{P}^S(\mathbb{C}^n)$ consisting of all…

A topological space is locally equiconnected if there exists a neighborhood $U$ of the diagonal in $X\times X$ and a continuous map $\lambda:U\times[0,1]\to X$ such that $\lambda(x,y,0)=x$, $\lambda(x,y,1)=y$ et $\lambda(x,x,t)=x$ for…

For a locally convex Lie group with the Trotter property, we prove that the space of k-times differentiable vectors of a unitary representation is equal to the intersection of domains of k-fold products of the Lie algebra action. The result…

Using the completed inductive, projective and injective tensor products of Grothendieck for locally convex topological vector spaces, we develop a systematic theory of locally convex Hopf algebras with an emphasis on Pontryagin-type…

We show that the incompressible Euler equations on $\mathbb{R}^2$ are not locally well-posed in the sense of Hadamard in the Besov space $B^1_{\infty,1}$. Our approach relies on the technique of Lagrangian deformations of Bourgain and Li.…

Motivated by the question of Mikael de la Salle, we investigate the problem of the existence of equivalent strictly convex norms on Banach spaces that are invariant with respect to an action of a group by linear isometries. We develop…

Assume that $(X, d, \mu)$ is a space of homogeneous type in the sense of Coifman and Weiss. In this article, motivated by the breakthrough work of P. Auscher and T. Hyt\"onen on orthonormal bases of regular wavelets on spaces of homogeneous…

In this article I describe my recent geometric localization argument dealing with actions of NONcompact groups which provides a geometric bridge between two entirely different character formulas for reductive Lie groups and answers the…

With the aim of completing the previous study by A. Or{\l}owski and the author concerning intertwining maps between induced representations and conjugation representation, termed here weighted class operators, we compute the latter…

Let G be a locally compact non-compact group. We show that under a very mild assumption on the weight function w, the weighted group algebra L_1(G,w) is strongly Arens irregular in the sense of Dales-Lamb-Lau. To this end, we first derive a…

This paper explores the irreducible uniformly bounded weight modules of map extended Special Lie algebras and map extended Hamiltonian Lie algebras under some condition on the action of the Laurent polynomial ring A_{N}.

Uniform laws of large numbers form a cornerstone of Vapnik--Chervonenkis theory, where they are characterized by the finiteness of the VC dimension. In this work, we study uniform convergence phenomena in cartesian product spaces, under…

We discuss the possible relation between certain geometrical properties of the loop space and energy evolution of the cusped Wilson exponentials defined on the light-cone. Analysis of the area differential equations for this special class…

We introduce anisotropic H\"older spaces useful for the study of the regularity theory for non local kinetic operators $\mathcal{L}$ whose prototypal example is \begin{equation} \mathcal{L} u (t,x,v) = \int_{\mathbb{R}^d} \frac{C_{d,s}}{|v…

We provide sufficient conditions under which the center-outward distribution and quantile functions introduced in Chernozhukov et al.~(2017) and Hallin~(2017) are homeomorphisms, thereby extending a recent result by Figalli \cite{Fi2}. Our…

We consider a class of generalized nonexpansive mappings introduced by Karapinar [5] and seen as a generalization of Suzuki (C)-condition. We prove some weak and strong convergence theorems for approximating fixed points of such mappings…