On Fredholm Transformations in Yeh-Wiener Space.
AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO
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Let C sub Y denote the Yeh-Wiener space, i.e., the space of all real-valued continuous functions fx,y on I sup 2 identically equal to 0,1x0,1 such that f0,y fx,0 identically equal to 0, and a Gaussian measure defined on it so that the expected value Efx,y 0 and the covariance Efs,tfx,y 12mins,x.mint,y. Consider the Fredholm transformations of the type Tfx,y fx,y the integral over I sup 2 of Kx,y,s,tfs,tdsdt of C sub Y onto C sub Y. Under suitable assumptions on the kernel Kx,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
- Theoretical Mathematics