Abstract. It is known that the structure of invariant subspaces of the Hardy space H 2 (D n ) on the polydisc D n is very complicated; hence, we need good examples help us to understand the structure of invariant subspaces of H 2 (D n ). In this paper, we define two types of invariant subspaces of H 2 (D n ). Then, we give a characterization of these types invariant subspaces in view of the Beurling-Lax-Halmos Theorem. Unitary equivalence is also studied in this paper.
In this paper we prove an invertibility criterion for certain operators which is given as a linear algebraic combination of Toeplitz operators and Fourier multipliers acting on the Hardy space of the unit disc. Very similar to the case of Toeplitz operators we prove that such operators are invertible if and only if they are Fredholm and their Fredholm index is zero. As an application we prove that for "quasi-parabolic" composition operators the spectra and the essential spectra are equal.2000 Mathematics Subject Classification. 47B33.
In this paper we present a new method for solving general singular equations of normal type. As an application of this method, we give a solution for a class of convolution-type integral equations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.