On Fredholm Transformations in Yeh-Wiener Space.
Abstract
Let C sub Y denote the Yeh-Wiener space, i.e., the space of all real-valued continuous functions f(x,y) on (I sup 2) identically equal to (0,1)x(0,1) such that f(0,y) = f(x,0) identically equal to 0, and a Gaussian measure defined on it so that the expected value E(f(x,y)) = 0 and the covariance E(f(s,t)f(x,y)) = (1/2)min(s,x).min(t,y). Consider the Fredholm transformations of the type T(f(x,y)) = f(x,y) + the integral over I sup 2 of K(x,y,s,t)f(s,t)dsdt of C sub Y onto C sub Y. Under suitable assumptions on the kernel K(x,y,s,t) the author gives the corresponding Radon-Nikodym derivatives. The author hopes the result will help for the evaluation of numerous Yeh-Wiener integrals of exponential functions. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1970
- Accession Number
- AD0718425
Entities
People
- Chull Park
Organizations
- Air Force Research Laboratory