Abstract
Starting with a Hilbert space L 2( R,μ) we introduce the dense subspace R( L 2( R,μ)) where R is a positive self-adjoint Hilbert–Schmidt operator on L 2( R ,μ). For the space R( L 2( R,μ)) a measure-theoretical Sobolev lemma is proved. The results for the spaces of type R( L 2( R,μ)) are applied to nuclear analyticity spaces S X, A = ⋃ t>0 e -t A (X) , where e −t A is a Hilbert–Schmidt operator on the Hilbert space X for each t>0. We solve the so-called generalized eigenvalue problem for a general self-adjoint operator P in X.
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