J Austral Math Soc Ser A 56 pp17--40, 1994.

Integration with Respect to Vector Valued Radon Polymeasures

Brian Jefferies and Werner J. Ricker

Abstract

Problems dealing with certain functional calculi for systems of non-commuting operators, and ordered calculi for systems of certain types of pseudo-differential operators, can sometimes be treated via the methods of integration with respect to polymeasures. The polymeasures arising in this fashion (called Radon polymeasures) often have additional structure not available in the general theory. This allows for a more extensive class of "integrable" functions than just the product functions allowed in the abstract theory. The purpose here is to further develop special aspects of integration with respect to Radon polymeasures with a particular emphasis on identifying large classes of "integrable" functions.

1991 AMS Subject Classification: 28B05, 28C15

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Authors

Brian Jefferies

School of Mathematics, University of New South Wales. P.O. Box 1, Kensington, N.S.W. Australia.

Werner J. Ricker

School of Mathematics, University of New South Wales. P.O. Box 1, Kensington, N.S.W. Australia.