TY - JOUR
T1 - Resonance eigenfunctions of a dilation-analytic Schrödinger operator, based on the Mellin transform
AU - Skibsted, Erik
PY - 1986/7
Y1 - 1986/7
N2 - We consider a dilation-analytic Schrödinger operator represented (by the Mellin transform) in the space HM{colon equals}{f:R→h|f is measurable and ∫∞-∞{norm of matrix}f(λ){norm of matrix}2hdλ<∞}, h is L2(S2), where S2 is the unit sphere in R3. In this representation a notion of resonance eigenfucntions is defined by using a certain Gelfand triple. We find an isomorphic connection between the space of resonance eigenfunctions and the space N(HM(θ) - z0), Im θ > - 1 2Arg z 0, where N(HM(θ) - z0) is the space of eigenfunctions associated with a resonance z0 and the θ-dilated operator HM(θ) in the space HM.
AB - We consider a dilation-analytic Schrödinger operator represented (by the Mellin transform) in the space HM{colon equals}{f:R→h|f is measurable and ∫∞-∞{norm of matrix}f(λ){norm of matrix}2hdλ<∞}, h is L2(S2), where S2 is the unit sphere in R3. In this representation a notion of resonance eigenfucntions is defined by using a certain Gelfand triple. We find an isomorphic connection between the space of resonance eigenfunctions and the space N(HM(θ) - z0), Im θ > - 1 2Arg z 0, where N(HM(θ) - z0) is the space of eigenfunctions associated with a resonance z0 and the θ-dilated operator HM(θ) in the space HM.
UR - https://www.scopus.com/pages/publications/46149131734
U2 - 10.1016/0022-247X(86)90256-8
DO - 10.1016/0022-247X(86)90256-8
M3 - Journal article
AN - SCOPUS:46149131734
SN - 0022-247X
VL - 117
SP - 198
EP - 219
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -