6533b828fe1ef96bd1288dae
RESEARCH PRODUCT
Non-Periodic Systems with Continuous Diffraction Measures
Michael BaakeUwe GrimmMatthias Birknersubject
Random measureMathematical analysisComplex measureInformation theory and measure theoryInvariant measureStatistical physicsDiscrete measureEmpirical measureMeasure (mathematics)Point processMathematicsdescription
The present state of mathematical diffraction theory for systems with continuous spectral components is reviewed and extended. We begin with a discussion of various characteristic examples with singular or absolutely continuous diffraction, and then continue with a more general exposition of a systematic approach via stationary stochastic point processes. Here, the intensity measure of the Palm measure takes the role of the autocorrelation measure in the traditional approach. We furthermore introduce a ‘Palm-type’ measure for general complex-valued random measures that are stationary and ergodic, and relate its intensity measure to the autocorrelation measure.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-01-01 |