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Publications Influence

Quantization on Nilpotent Lie Groups

- Veronique Fischer, Michael Ruzhansky
- Mathematics
- 22 March 2016

Preface.- Introduction.- Notation and conventions.- 1 Preliminaries on Lie groups.- 2 Quantization on compact Lie groups.- 3 Homogeneous Lie groups.- 4 Rockland operators and Sobolev spaces.- 5… Expand

151 12- PDF

Pseudo-differential operators on the Heisenberg group

- Veronique Fischer, Michael Ruzhansky
- Political Science
- 1 March 2016

The Heisenberg group was introduced in Example 1.6.4. It was our primal example of a stratified Lie group, see Section 3.1.1. Due to the importance of the Heisenberg group and of its many… Expand

8 3

Lower bounds for operators on graded Lie groups

- Veronique Fischer, Michael Ruzhansky
- Mathematics
- 3 January 2013

Abstract In this note we present a symbolic pseudo-differential calculus on any graded (nilpotent) Lie group and, as an application, a version of the sharp Garding inequality. As a corollary, we… Expand

12 2- PDF

Semi-classical analysis on H-type groups

- C. Kammerer, Veronique Fischer
- Mathematics
- 30 November 2018

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… Expand

8 2- PDF

Intrinsic pseudo-differential calculi on any compact Lie group

- Veronique Fischer
- Mathematics
- 27 September 2014

Abstract In this paper, we define in an intrinsic way operators on a compact Lie group by means of symbols using the representations of the group. The main purpose is to show that these operators… Expand

19 1- PDF

The bounded spherical functions for the free two step nilpotent Lie group

- Veronique Fischer
- Mathematics
- 3 February 2006

In this paper, we give the expressions for the bounded spherical functions, or equivalently the spherical functions of positive type, for the free two-step nilpotent Lie groups endowed with the… Expand

4 1- PDF

A pseudo-differential calculus on the Heisenberg group

- Veronique Fischer, Michael Ruzhansky
- Mathematics
- 26 February 2014

In this note we present a symbolic pseudo-differential calculus on the Heisenberg group. We particularise to this group our general construction [4,2,3] of pseudo-differential calculi on graded… Expand

20 1- PDF

Sobolev spaces on graded lie groups

- Veronique Fischer, Michael Ruzhansky
- Mathematics
- 1 July 2017

— In this article, we study the Lp-properties of powers of positive Rockland operators and define Sobolev spaces on general graded Lie groups. We establish that the defined Sobolev spaces are… Expand

14 1- PDF

The Heisenberg oscillator

- Veronique Fischer
- Physics, Mathematics
- 16 August 2011

In this short note, we determine the spectrum of the Heisenberg oscillator which is the operator defined as $$L+|x|^2+|y|^2$$ on the Heisenberg group $$H_1=\mathbb{ R} ^2_{x,y}\times \mathbb{ R} $$… Expand

2 1- PDF

Differential structure on the dual of a compact lie group

- Veronique Fischer
- Mathematics
- 20 October 2016

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,… Expand

4 1- PDF

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