ABSTRACT
COROLLARY III.l. Assume, in Theorem III.1, that Y = X, and that A (H(R)) H(R) with the corresponding embedding H(R) X being continuous.
Denote by xn, n = 1, 2, . . . the process Anx, and let Kn be the covariance of the process xn. Let Hn be the RKHS with the kernel Kn. If the sample paths of x1 = Ax belong to H(R), then the sample paths of the process xn belong almost surely to the RKHS Hn-1, n = 2,3 ...
