Toeplitz operators on the space of all entire functions
type: Item
instance of: scholarly article
title: Toeplitz operators on the space of all entire functions
author: Michał Jasiczak
published in: The New York Journal of Mathematics
publication date: 2020-07-29T00:00:00Z
full work available at URL: 26-34.html
review text: There are introduced and analyzed Toeplitz operators on the Fréchet space \(H(\mathbb{C})\) of entire functions. These operators are defined as linear continuous operators on \(H(\mathbb{C})\) with Toeplitz matrices with respect to the basis \(\lbrace z^n\rbrace_{n\ge0}\). There is obtained a representation of such operators as a product of a multiplication operator by an entire function and some Cauchy transform. The symbol space of these operators is the space \(H(\mathbb{C})\oplus H_0(\infty)\) where \(H_0(\infty)\) is the space of all germs at \(\infty\) of holomorphic functions vanishing at this point. There are characterized Fredholm, semi-Fredholm and one-sided invertible operators from this class. There is found index of Fredholm operator.
reviewed by: Vladimir S. Pilidi
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 30H99
Mathematics Subject Classification ID: 47A53
zbMATH DE Number: 7225798
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: entire function
zbMATH Keywords: Fredholm
zbMATH Keywords: semi-Fredholm
zbMATH Keywords: index
zbMATH Keywords: one-sided invertible
zbMATH Keywords: Cauchy transform
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7225798