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Norm bounds for self-adjoint Toeplitz operators with non-radial symbols on the Fock space

Published 18 May 2024 in math.FA | (2405.11147v1)

Abstract: In this paper we extend Galbis' elegant norm bounds for self-adjoint Toeplitz operators on the Fock space to bounded and integrable symbols which are non-radial. The main ingredients are a transplantation of the remarkable Nicola-Tilli isoperimetric inequality to the realm of Fock-Toeplitz operator theory and a two-dimensional adaption of Galbis' integration and approximation arguments.

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References (7)
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  2. A. Galbis. Norm estimates for selfadjoint Toeplitz operators on the Fock space. Complex Analysis and Operator Theory, 16(1):15, 2022.
  3. Stability of the Faber-Krahn inequality for the short-time Fourier transform. Inventiones Mathematicae, 236(2):779–836, 2024.
  4. Toeplitz operators on the Fock space: radial component effects. Integral Equations and Operator Theory, 44(1):10–37, 2002.
  5. A. Kulikov. Functionals with extrema at reproducing kernels. Geometric and Functional Analysis, 32(4):938–949, 2022.
  6. F. Nicola and P. Tilli. The Faber–Krahn inequality for the short-time Fourier transform. Inventiones Mathematicae, 230(1):1–30, 2022.
  7. K. Zhu. Analysis on Fock spaces, volume 263 of Graduate Texts in Mathematics. Springer, 2012.

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