Master of Science
Gilbert A. Stengle
The object ofthis paper is to establish that the power series of a certain functions on Hilbert space with Gaussian measure are pointwise convergent. The main result states that the power series of such functions converges uniformly on the image of a sphere under a certain mapping in the definition of the measure. This region looks like an ellipse with the axes tending to zero in higher dimensions.
Landis, Dale, "Square integrable analytic functions on hilbert spaces with gaussian measure and pointwise convergence of fourier series" (1966). Theses and Dissertations. 3416.