## Spectral Theory For Random Closed Sets And Estimating The Covariance Via Frequency Space

• A spectral theory for stationary random closed sets is developed and provided with a sound mathematical basis. Definition and proof of existence of the Bartlett spectrum of a stationary random closed set as well as the proof of a Wiener-Khintchine theorem for the power spectrum are used to two ends: First, well known second order characteristics like the covariance can be estimated faster than usual via frequency space. Second, the Bartlett spectrum and the power spectrum can be used as second order characteristics in frequency space. Examples show, that in some cases information about the random closed set is easier to obtain from these characteristics in frequency space than from their real world counterparts.

Author: K. Koch, J. Ohser, K. Schladitz urn:nbn:de:hbz:386-kluedo-12998 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (37) Report English 2002 2002 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik 2004/02/02 Bartlett spectrum; Random set; fast Fourier transform; power spectrum Fraunhofer (ITWM) 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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