Decompositions of Gelfand-Shilov kernels into kernels of similar class

2011/12/19 by Joachim Toft, Andrei Khrennikov, Toft, Joachim +5
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA

paper · pdf · doi:10.48550/arxiv.1112.4314

13 pages. arXiv admin note: text overlap with arXiv:1102.0336

arxiv created 2012/05/10 · arxiv updated 2012/05/11

Abstract

We prove that any linear operator with kernel in a Gelfand-Shilov space is a composition of two operators with kernels in the same Gelfand-Shilov space. We also give links on numerical approximations for such compositions. We apply these composition rules to establish Schatten-von Neumann properties for such operators.

Citations

• The Bargmann transform on a broad family of Banach spaces, with applications to Toeplitz and pseudo-differential operators

Related

• Factorizations and singular value estimates of operators with Gelfand-Shilov and Pilipović kernels
• Composition operators on Gelfand-Shilov classes
• Topologizability and related properties of the iterates of composition operators in Gelfand-Shilov classes
• Gelfand-Shilov spaces, Structural and Kernel theorems
• Fourier characterizations and non-triviality of Gelfand-Shilov spaces, with applications to Toeplitz operators