6533b855fe1ef96bd12b065b
RESEARCH PRODUCT
Time operators, innovations and approximations
Ioannis AntoniouIoannis AntoniouZ. SuchaneckiZ. Suchaneckisubject
Dynamical systems theoryStochastic processSemigroupGeneral MathematicsApplied MathematicsMathematical analysisTime evolutionGeneral Physics and AstronomyStatistical and Nonlinear PhysicsSpectral theoremOperator theoryOperator (computer programming)Applied mathematicsRepresentation (mathematics)Mathematicsdescription
Abstract We present a new approach to the spectral analysis and prediction of such complex systems for which the time evolution is described by a semigroup of operators. This approach is based on an extended concept of time operator and can be interpreted as a shift representation of dynamical systems. The time operator method includes the multiresolution analysis of wavelets as a particular case but can also be applied for a substantially larger class of dynamical systems. Among the examples where shift representation have been explicitly derived are exact endomorphisms, the diffusion equation, generalized shifts associated with the Haar or Faber–Schauder basis and some classes of stochastic processes.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-07-01 | Chaos, Solitons & Fractals |