ABSTRACT
Proposition III.7 Let x be a regular CS(N) numerical sequence having autocorrelation R(N)m,n (x) and let J be the map from MN (X) into sp{xk, k Î Z} Ì H (x) defined for arbitrary complex l, µ and integers k, p by
J (lSpx + µ S k x ) = lxp + µxk.. (3.37) Then J can be extended as an isometric Hilbert space isomorphism from a
complex Hilbert space HN (X) containing MN to the complex Hilbert space H (x), the closed linear span of a CS stochastic process x that has autocorrelation function
completion [26, p. 121, 124 - 125], the proposition holds through the continuity (boundedness) of J on MN (x).
