6533b839fe1ef96bd12a5ab4

RESEARCH PRODUCT

Characterizing boundedness of metaplectic Toeplitz operators

Lewis CoburnMichael HitrikJohannes Sjoestrand

subject

Mathematics - Functional Analysis32A36 32U05 32W25 35S30 47B35Mathematics - Complex VariablesFOS: MathematicsComplex Variables (math.CV)Functional Analysis (math.FA)

description

We study Toeplitz operators on the Bargmann space, with Toeplitz symbols given by exponentials of complex quadratic forms. We show that the boundedness of the corresponding Weyl symbols is necessary for the boundedness of the operators, thereby completing the proof of the Berger-Coburn conjecture in this case. We also show that the compactness of such Toeplitz operators is equivalent to the vanishing of their Weyl symbols at infinity.

yearjournalcountryeditionlanguage
2023-03-02
http://arxiv.org/abs/2303.01558