How to define the Fourier transform on Heisenberg groups
Speaker: Sundaram Thangavelu
Affiliation: Indian Institute of Science
Abstract
The usual definition of Fourier transform on the Heisenberg $ \mathbb{H}^n $ is in terms of the Schr\"odinger representations $ \pi_\lambda $ which makes it operator valued and hence unwieldy and not suitable for studying several problems in harmonic analysis on $ \mathbb{H}^n.$ In this talk, which is based on a recent article, we propose a scalar valued Fourier transform that shares several properties with the Helgason Fourier transform on noncompact rank one Riemannian symmetric spaces.
References
S. Thangavelu, A scalar valued Fourier transform for the Heisenberg group arXiv:2206.00883
About Pure mathematics seminars
We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.
Seminars are usually held on Tuesdays from 2 to 3pm.
Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.
Information for speakers
Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.
Contact us
To volunteer to talk or to suggest a speaker, email Ole Warnaar or Ramiro Lafuente.