Finite Rank Bargmann-Toeplitz Operators with Non-Compactly Supported Symbols

2012/03/22 by Grigori Rozenblum, Rozenblum, Grigori
Mathematics · #46J10 #47B35 #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #math.CV #math.FA #msc:46J10 #msc:47B35

paper · pdf · doi:10.48550/arxiv.1203.4927

openalex publication_date 2012/03/22 · arxiv created 2012/03/25 · arxiv updated 2012/03/27 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28

Abstract

Theorems about characterization of finite rank Toeplitz operators in Fock-Segal-Bargmann spaces, known previously only for symbols with compact support, are carried over to symbols without that restriction, however with a rather rapid decay at infinity. The proof is based upon a new version of the Stone-Weierstrass approximation theorem.

Citations

• Finite rank Bergman-Toeplitz and Bargmann-Toeplitz operators in many dimensions

Related

• The finite rank theorem for Toeplitz operators in the Fock space
• Finite Rank Toeplitz Operators: Some Extensions of D.Luecking's Theorem
• Finite rank Toeplitz operators in Bergman spaces
• Finite rank Bergman-Toeplitz and Bargmann-Toeplitz operators in many dimensions
• Truncated Toeplitz operators of finite rank