Toeplitz operators on the space of all entire functions
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.
scientific article; zbMATH DE number 7225798
scientific article