Accession Number : AD0718425

Title :   On Fredholm Transformations in Yeh-Wiener Space.

Descriptive Note : Final rept.,

Corporate Author : AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO

Personal Author(s) : Park,Chull

Report Date : NOV 1970

Pagination or Media Count : 32

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)

Descriptors :   (*INTEGRAL TRANSFORMS, THEOREMS), (*INTEGRAL EQUATIONS, THEOREMS), EXPONENTIAL FUNCTIONS, DETERMINANTS(MATHEMATICS), MEASURE THEORY, NUMERICAL INTEGRATION

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE