On adiabatic reduction theory. (English) Zbl 0897.47036

Martinez, A.; Nenciu, G.

Demuth, M. (ed.) et al., Partial differential operators and mathematical physics. International conference in Holzhau, Germany, July 3-9, 1994. Basel: Birkhäuser Verlag. Oper. Theory, Adv. Appl. 78, 243-252 (1995).

The authors study an evolution process implemented by an operator family holomorphic in a strip around the real axis, and satisfying additional conditions. In particular, the values on the real axis are selfadjoint, with spectra having a gap of length greater than a fixed positive number. The behaviour of the corresponding spectral projections is analyzed and a certain reduction is studied.
For the entire collection see [Zbl 0815.00009].

Reviewer: J.Zemánek (Warszawa)

MSC:

47D06

One-parameter semigroups and linear evolution equations

Keywords:

evolution process; operator family holomorphic in a strip around the real axis; selfadjoint; spectral projections