Remarks on the HRT Conjecture

Chapter

Abstract

Motivated by a conjecture about time-frequency translations of functions, several properties of the Bargmann–Fock space \(\mathcal{H}\) and the Segal–Bargmann transform \(\mathcal{S}\) are investigated in this note. In particular, a characterization is given of those square integrable functions \(\varphi\) on \(\mathbb{R}\) such that \(z \in \mathbb{C}\longmapsto \mathcal{S}\varphi (z+\zeta ) \in \mathbb{C}\) is in \(\mathcal{H}\) for all \(\zeta \in \mathbb{C}\).

References

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.M.I.T.CambridgeUSA

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