Resonance eigenfunctions of a dilation-analytic Schrödinger operator, based on the Mellin transform

AbstractWe consider a dilation-analytic Schrödinger operator represented (by the Mellin transform) in the space HM≔{f:R→h|f is measurable and ∫∞−∞‖f(λ)‖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 > − 12Arg 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