Vol. 66, No. 2, 1976

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ISSN: 0030-8730
On Cameron and Storvick’s operator valued function space integral

Katsuo Takano

Vol. 66 (1976), No. 2, 561–591
Abstract

In this paper “the probability density of path space” is introduced by the formula

           ∫
α       -1  ∞            t  α
pλ(t,u) = 2π −∞ exp(− iu η− λ|η|)dη,  (α > 0).

If α = 2 and λ > 0, pλα(t,u) is the normal probability density. But if α > 2 this density can not be considered as a probability density. By this generalization, one can generalize the operator valued function space integral based on the Wiener integral.

Mathematical Subject Classification
Primary: 28A40, 28A40
Milestones
Received: 18 July 1975
Revised: 12 May 1976
Published: 1 October 1976
Authors
Katsuo Takano