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 -