Abstract:

Under the classical differential sense, the Toeplitz operator with general symbol on the Dirichlet space is defined by directly using  integral. And a class of continuous symbols is introduced. Toeplitz operators on the Dirichlet space with these symbols are considered, obtaining the sufficient conditions for finite rank Toeplitz operators and zero product pro
blems on the Dirichlet space.

Key words: Toeplitz operator, Dirichlet space, quasihomogeneous symbols, finite rank, zero product