Véronique Fischer's research while affiliated with University of Bath and other places

Publications (3)

Preprint
Full-text available
In this paper, we consider the semi-classical setting constructed on nilpotent graded Lie groups by means of representation theory. We analyze the effects of the pull-back by diffeomorphisms on pseudodifferential operators. We restrict to diffeomorphisms that preserve the filtration and prove that they are Pansu differentiable. We show that the pul...
Article
In this paper we define difference operators and homogeneous Sobolev-type spaces on the dual of a compact Lie group. As an application and to show that this defines a relevant differential structure, we state and prove multiplier theorems of Hörmander, Mihlin and Marcinkiewicz types together with the sharpness in the Sobolev exponent for the result...
Article
In this paper, we develop semi-classical analysis on H-type groups. We define semi-classical pseudodi fferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic calculus. Then, we define the semi-classical measures of bounded families of square integrable functions which consist of a pair forme...

Citations

... To our best knowledge, the first study of Fourier multipliers on Lie groups was done by Coifman and Weiss in [13], where they developed Calderón-Zygmund theory on spaces of homogeneous type and as an application they studied the Fourier multipliers of SU(2), see also [14]. After that, investigations of Fourier multipliers on compact Lie groups has been focused on the central multipliers [48,50,51,52], untill the appearance of the recent works of Ruzhansky and Wirth [46,47] and Fischer [21]. The rest of the literature concerning Fourier multipliers on Lie groups is restricted to the motion group [45] and to the Heisenberg group [15]. ...
... In this section, we will present the works [24,25,26] of Clotilde Fermanian-Kammerer and the author about quantum limits on nilpotent Lie groups. We will only describe briefly the setting and the notation, referring the interested reader to the literature for all the technical details. ...