Shift invariant spaces and prediction theory

Beurling, A., On two problems concerning linear transformations in Hilbert space.Acta Math., 81 (1949), 239–255. Doob, J. L.,Stochastic Processes. New York, 1953. Halmos, P., Shifts of Hilbert spaces.Crelle's Journal, 208 (1961), 102–112. Helson, H. &Lowdenslager, D., Prediction theory and Fourier series in several variables.Acta Math., 99 (1958), 165–202. Hoffman, K.,H p Spaces. Mass. Inst. of Technology, Cambridge, Mass., 1961 (mimeographed). Kolmogorov, A. N., Stationary sequences in Hilbert space (Russian).Bull. Math. Univ. Moscou, 2, No. 6 (1951), 40 pp. (English translation by Natasha Artin.) Lax, P., Translation invariant subspaces.Acta Math., 101 (1959), 163–178. Masani, P.,Cramer's Theorem on monotone matrix-valued functions and the Wold docomposition, Probability and Statistics, the Harald Cramer Volume, Ed. Ulf Grenander, Stockholm, 1959, pp. 175–189. —, Sur la fonction génératrice d'un processus stochastique vectoriel.C. R. Acad. Sci. Paris, 249 (1959), 360–362. —, Isomorphie entre les domaines temporel et spectral d'un processus vectoriel, régulier.C. R. Acad. Sci. Paris, 249 (1959) 496–498. Masani, P., Sur les fonctions matricielles de la classe de Hardy H2.C. R. Acad. Sci. Paris, 249 (1959), 873–875. —, Sur les fonctions matricielles de la classe de Hardy H2.C. R. Acad. Sci. Paris, 249 (1959), 906–907. —, Une généralisation pour les fonctions matricielles de la classe de Hardy H2 d'un théorème de Nevanlinna,C. R. Acad. Sci. Paris, 251 (1960), 318–320. —, The prediction theory of multivariate stochastic processes, III.Acta Math., 104 (1960), 141–162. Masani, P. &Wiener, N.,On bivariate stationary processes and the factorization of matrix-valued functions.Theory of Probability and its Applications, IV (1959), 300–308. Potapov, V. P., The multiplicative structure ofJ-contractive matrix functions.Trudi Mosk. Matem. Obsch, 4 (1955), 125–236. (In Russian.) (Amer. Math. Soc. Transl., 15 (1960), 131–243.) Rozanov, Yu. A., The spectral theory of multi-dimensional stationary stochastic processes with discrete time.Uspekhi Mat. Nauk, XXIII, (1957), 989–992. (In Russian). Wiener, N. &Masani, P., The prediction theory of multivariate stochastic processes, Part I.Acta Math., 98 (1957), 111–150, Part II,Acta Math., 99 (1958) 93–137.