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arXiv · 2306.14188

Boundedness of certain linear operators on twisted Fock spaces

Rahul Garg·Sundaram Thangavelu
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Abstract

On the twisted Fock spaces $ \mathcal{F}^\lambda(\mathbb{C}^{2n}) $ we consider two types of convolution operators $ S_\varphi $ and $ \widetilde{S}_\varphi $ associated to an element $ \varphi \in \mathcal{F}^\lambda(\mathbb{C}^{2n}) .$ We find a necessary and sufficient condition on $ \varphi $ so that $ S_\varphi $ (resp. $ \widetilde{S}_\varphi $ ) is bounded on $ \mathcal{F}^\lambda(\mathbb{C}^{2n}).$ We show that for any given non constant $ \varphi $ at least one of these two operators is unbounded.

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Rahul Garg, Sundaram Thangavelu. 2023-06-25. Boundedness of certain linear operators on twisted Fock spaces. https://doi.org/10.1007/s00209-024-03500-0

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