Characterizations of Fock-type spaces of eigenfunctions on Rⁿ

Abstract

In this paper, we prove a norm equivalence for an exponential type weighted integral of an eigenfunction and its derivative on Rn. As applications, we characterize Fock-type spaces of eigenfunctions on Rn in terms of Lipschitz type conditions and double integral conditions. These obtained results are extensions of the corresponding ones in classcial Fock space.

Keywords

• eigenfunction
• fock space
• lipschitz condition
• double integral condition