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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

Pseudo-differential operators on the Heisenberg group

- Veronique Fischer, Michael Ruzhansky
- Mathematics
- 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

Intrinsic pseudo-differential calculi on any compact Lie group

- Veronique Fischer
- Mathematics
- 27 September 2014

Lower bounds for operators on graded Lie groups

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

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

A Pseudo-differential Calculus on Graded Nilpotent Lie Groups

- Veronique Fischer, Michael Ruzhansky
- Mathematics
- 12 September 2012

In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using… Expand

A pseudo-differential calculus on the Heisenberg group

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

Gelfand transforms of SO(3)-invariant Schwartz functions on the free group N_{3,2}

- Veronique Fischer, F. Ricci
- Mathematics
- 11 September 2008

The spectrum of a Gelfand pair $(K\ltimes N, K)$, where $N$ is a nilpotent group, can be embedded in a Euclidean space. We prove that in general, the Schwartz functions on the spectrum are the… Expand

Heisenberg-Modulation Spaces at the Crossroads of Coorbit Theory and Decomposition Space Theory.

- Veronique Fischer, David Rottensteiner, Michael Ruzhansky
- Mathematics
- 19 December 2018

We show that generalised time-frequency shifts on the Heisenberg group $\mathbf{H}_n \cong \mathbb{R}^{2n+1}$, realised as a unitary irreducible representation of a nilpotent Lie group acting on… Expand

The Heisenberg oscillator

- Veronique Fischer
- 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

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