TY - JOUR

T1 - A mathematical interpretation of Dirac's formalism. Part B: Generalized eigenfunctions in trajectory spaces

AU - Eijndhoven, van, S.J.L.

AU - Graaf, de, J.

PY - 1985

Y1 - 1985

N2 - Starting with a Hilbert space we introduce the dense subspace where is a positive self-adjoint Hilbert–Schmidt operator on 2(R,µ). For the space a measure-theoretical Sobolev lemma is proved. The results for the spaces of type are applied to nuclear analyticity spaces , where e-t 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 in X.

AB - Starting with a Hilbert space we introduce the dense subspace where is a positive self-adjoint Hilbert–Schmidt operator on 2(R,µ). For the space a measure-theoretical Sobolev lemma is proved. The results for the spaces of type are applied to nuclear analyticity spaces , where e-t 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 in X.

U2 - 10.1016/0034-4877(85)90049-7

DO - 10.1016/0034-4877(85)90049-7

M3 - Article

SN - 0034-4877

VL - 22

SP - 189

EP - 203

JO - Reports on Mathematical Physics

JF - Reports on Mathematical Physics

IS - 2

ER -