In the theory of N-body Schrödinger operators the concept of
dilation analyticity introduced by Aguilar and Combes and Balslev and Combes
had tremendous success in studying the essential spectrum of such operators.
The key idea in these two papers is that the unitary group of dilations can be
used to transform the Schrödinger operator into a one parameter family of
operators which admits an analytic continuation into a strip in the complex plane.
The virtue of this continuation is that its essential recedes from the real line
making a more detailed analysis possible. An application of this concept to time
dependent perturbation theory inquantum mechanics was later derived by Simon.
The generator of the group of dilations turns out to be a conjugate operator for
the Schrödinger operator under examination. This leads us to the question,
whether the techniques developed by Balslev and Combes can be done in an abstract
framework starting from Mourre theory. In this talk an affirmative answer is
provided in a systematic fashion by replacing the group of dilations with the
unitary group generated by an abstract conjugate operator. Key ingredients are
the use of the Mourre estimate and known results on abstract spectral deformation
techniques by Hunziker and Sigal.