Abstract
<abstract><p>In this paper, we prove a norm equivalence for an exponential type weighted integral of an eigenfunction and its derivative on $ \mathbb{R}^n $. As applications, we characterize Fock-type spaces of eigenfunctions on $ \mathbb{R}^n $ in terms of Lipschitz type conditions and double integral conditions. These obtained results are extensions of the corresponding ones in classcial Fock space.</p></abstract>
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