2019/05/19 by Johannes Keller, Keller, Johannes, Franz Luef +1
Mathematics · #32A36 #46E22 #81Q20 #81Sxx #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1905.07741
openalex publication_date 2019/05/19 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
We discuss an extension of Toeplitz quantization based on polyanalytic\nfunctions. We derive isomorphism theorem for polyanalytic Toeplitz operators\nbetween weighted Sobolev-Fock spaces of polyanalytic functions, which are\nimages of modulation spaces under polyanalytic Bargmann transforms. This\ngeneralizes well-known results from the analytic setting. Finally, we derive an\nasymptotic symbol calculus and present an asymptotic expansion of complex Weyl\noperators in terms of polyanalytic Toeplitz operators.\n