| The Dirichlet space D is the space of all analytic functions f on the open unit disc D,that have a finite Dirichlet integral,i.e.D={f∈Hol(D):∫D|f’(z)|2dA(z)<∞},The Dirichlet space is one of the classical analytic Hilbert space over D.(The other two are Hardy space and Bergman space).We call an invariant subspace of operator Mz an invariant subspace of Dirichlet space.This paper focus on the classification of invariant subspace of D under the similarity.We proved that two invariant subspaces M=[f]=fD(mf),N=[g]=gD(mg),are similar if and only if there exists a multiplier h of Dirichlet type space:D(mf)→D(mg),and makes... |
