Applications of autoreproducing kernel grammian moduli to (U, H)-valued stationary random functions

It is shown that the analytical characterizations of q-variate interpolable and minimal stationary processes obtained by H. Salehi (Ark. Mat., 7 (1967), 305-311; Ark. Mat., 8 (1968), 1-6; J. Math. Anal. Appl., 25 (1969), 653-662), and later by A. Weron (Studia Math., 49 (1974), 165-183), can be easily extended to Hilbert space valued stationary processes when using the two grammian moduli that respectively autoreproduce their correlation kernel and their spectral measure. Furthermore, for these processes, a Wold-Cramér concordance theorem is obtained that generalizes an earlier result established by H. Salehi and J. K. Scheidt (J. Multivar. Anal., 2 (1972), 307-331) and by A. Makagon and A. Weron (J. Multivar. Anal., 6 (1976), 123-137).