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Classes of Trimeasures: Applications of Harmonic Analysis

In: Probability Measures on Groups X

Author

Listed:
  • Colin C. Graham

    (Northwestern University, Department of Mathematics
    Lakehead University, Department of Mathematics)

  • Kari Ylinen

    (University of Turku, Department of Mathematics)

Abstract

Let X1,... ,X n be locally compact Hausdorff spaces and C 0 (X i ) the commutative C*-algebra of continuous complex functions on X i vanishing at infinity for i = 1,..., n. A bounded n-linear form Ф : C 0 (X 1 ) × × C 0 (X n ) → C will be called a polymeasure. (The term muliimeasure also appears in the literature as a synonym, but we avoid it in order not to conflict with its other uses.) The Banach space of such polymeasures equipped with the usual supremum norm ∥•∥ we denote by PM(X1,... ,Xn). The cases n = 2 (bimeasures) and especially n = 3 (trimeasures) are of particular interest to us.

Suggested Citation

  • Colin C. Graham & Kari Ylinen, 1991. "Classes of Trimeasures: Applications of Harmonic Analysis," Springer Books, in: Herbert Heyer (ed.), Probability Measures on Groups X, pages 169-176, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-2364-6_13
    DOI: 10.1007/978-1-4899-2364-6_13
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