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The concept of a filter†

Published online by Cambridge University Press:  24 October 2008

E. J. Hannan
E. J. Hannan
Affiliation:
Australian National University
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Abstract

It is proved that for a second-order, homogeneous, random process on a globally symmetric space a filter, that is a closed linear operator which is invariant under a group of isometries of the space, may be fully described through a response function, that is that it has a direct integral decomposition into components which are scalar multiples of the identity.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 1 , January 1967 , pp. 221 - 227
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

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