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Remarks on the HRT Conjecture

  • Daniel W. Stroock
Part of the Lecture Notes in Mathematics book series (LNM, volume 2137)

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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    C. Heil, J. Ramanathan, Topiwala, Linear independent of time-frequency translates. Proc. Am. Math. Soc. 124(9), 2787–2795 (1996)zbMATHMathSciNetGoogle Scholar
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    I.E. Segal, Mathematical problems of relativistic physics, Chap. VI, in Proceedings of the Summer Seminar, Boulder, 1960, vol. II, ed. by M. Kac. Lectures in Applied Mathematics (American Mathematical Society, Providence, 1963)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.M.I.T.CambridgeUSA

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