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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.
Reference: S. Thangavelu, A scalar valued Fourier transform for the Heisenberg group arXiv:2206.00883 |