2023/05/06 by Haoren Xiong, Xiong, Haoren
Mathematics · #32A36 #32U05 #32W25 #35S30 #47B35 #Advanced Algebra and Geometry #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2305.03948
openalex publication_date 2023/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study Toeplitz operators on the Bargmann space, whose Toeplitz symbols are exponentials of complex inhomogeneous quadratic polynomials. Extending a result by Coburn--Hitrik--Sjöstrand, we show that the boundedness of such Toeplitz operators implies the boundedness of the corresponding Weyl symbols, thus completing the proof of the Berger--Coburn conjecture in this case. We also show that a Toeplitz operator is compact precisely when its Weyl symbol vanishes at infinity in this case.