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Innovative processes and the factorization problem

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Literature cited

  1. E. G. Gladyshev, “Multidimensional stationary random processes,” Teor. Veroyst. i ee Primen.,3, No. 4, 458–462 (1958).

    Google Scholar 

  2. K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, New Jersey (1962).

    Google Scholar 

  3. I. Ts. Gokhberg and M. G. Krein, Theory of Volterra Operators in Hilbert Space and Applications [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  4. N. Dunford and J. T. Schwartz, Linear Operators, Part I. General Theory, Wiley (1958).

  5. N. Dunford and J. T. Schwartz, Linear Operators. Part II. Spectral Theory. Self-Adjoint Operators in Hilbert Space, Wiley (1958).

  6. V. N. Zasukhin, “Theory of multidimensional stationary processes,” Dokl. Akad. Nauk,33, 435–437 (1941).

    Google Scholar 

  7. I. A. Ibragimov and Yu. A. Rozanov, Gaussian Random Processes [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  8. Z. Ivkovich and Yu. A. Rozanov, “Hida-Cramer canonical decomposition for random processes,” Teor. Veroyat. i ee Primen.,16, No. 2, 348–353 (1971).

    Google Scholar 

  9. A. N. Kolmogorov, “Stationary sequences in Hilbert space,” Byull. MGU,2, No. 6, 1–40 (1941).

    Google Scholar 

  10. M. G. Krein, “An extrapolation problem of A. N. Kolmogorov,” Dokl. Akad. Nauk SSSR,46, 306–309 (1944).

    Google Scholar 

  11. M. G. Krein, “Fundamental approximation problem of the theory of extrapolation and filtration of stationary random processes,” Dokl. Akad. Nauk SSSR,94, No. 1, 13–16 (1954).

    Google Scholar 

  12. V. I. Krylov, “Functions regular in the half-plane,” Matem. Sb.,4, No. 46, 9–30 (1938).

    Google Scholar 

  13. R. F. Matveev, “Regularity of multidimensional stationary processes,” Dokl. Akad. Nauk SSSR,126, No. 5 (1959).

  14. A. I. Plesner and V. A. Rokhlin, “Spectral theory of linear operators. II,” Usp. Matem. Nauk,1, No. 1, 71–191 (1946).

    Google Scholar 

  15. I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], Moscow-Leningrad (1950).

  16. F. Riesz and B. Sz.-Nagy, Functional Analysis, Ungar, New York.

  17. Yu. A. Rozanov, “Linear interpolation of stationary processes with discontinuous time,” Dokl. Akad. Nauk SSSR,116, No. 6, 923–926 (1957).

    Google Scholar 

  18. Yu. A. Rozanov, “Spectral theory of multidimensional stationary random processes with discontinuous time,” Usp. Matem. Nauk,13, No. 2, 93–142 (1958).

    Google Scholar 

  19. Yu. A. Rozanov, Stationary Random Processes [in Russian], Fizmatgiz, Moscow (1963).

    Google Scholar 

  20. Yu. A. Rozanov, “Gaussian infinite-dimensional distributions,” Tr. Matem. Institute Akad. Nauk SSSR,108 (1968).

  21. B. Sz.-Nagy and C. Foias, Harmonic Analysis of Operators on Hilbert Space, North-Holland, New York (1971).

    Google Scholar 

  22. H. Cramer, “Stochastic processes as curves in Hilbert space,” Teor. Veroyat. i ee Primen.,9, No. 2, 193–204 (1964).

    Google Scholar 

  23. A. Devinatz, “The factorization of operator valued functions,” Ann. Math.,73, No. 3, 458–495 (1961).

    Google Scholar 

  24. R. G. Douglas, “On factoring positive operator functions,” J. Math. and Mech.,16, No. 2, 119–126 (1966).

    Google Scholar 

  25. J. Feldman, “Equivalence and perpendicularity of Gaussian processes,” Pacif. J. Math.,8, No. 4, 699–708 (1958).

    Google Scholar 

  26. J. Feldman, “Some classes of equivalent Gaussian processes on an integral,” Pacif. J. Math.,10, No. 4, 1211–1220 (1960).

    Google Scholar 

  27. P. Halmos, Introduction to Hilbert Space and the Theory of Spectral Multiplicity, New York (1951).

  28. O. Hanner, “Deterministic and nondeterministic stationary random processes,” Ark. Mat.,1, No. 44, 161–177 (1950).

    Google Scholar 

  29. H. Helson and D. Lowdenslager, “Prediction theory and Fourier series in several variables. I,” Acta Math.,99, No. 3–4, 165–202 (1958).

    Google Scholar 

  30. H. Helson and D. Lowdenslager, “Prediction theory and Fourier series in several variables. II,” Acta Math.,106, Nos. 3–4, 175–213 (1961).

    Google Scholar 

  31. H. Helson, “Vector valued processes,” Proc. 4th Berkeley Sympos. Math. Statistics and Probability, 1960, Vol. 2, Univ. California Press, Berkeley-Los Angeles (1961), pp. 203–212.

    Google Scholar 

  32. T. Hida, “Canonical representations of Gaussian processes and their applications,” Mem. Coll. Sci. Univ. Kyoto, Ser. A,33, No. 1, 109–155 (1960).

    Google Scholar 

  33. G. Kallianpur and V. Mandrekar, “Multiplicity and representation theory of purely nondeterministic stochastic processes,” Teor. Veroyat. i ee Primen.,10, No. 4, 614–644 (1965).

    Google Scholar 

  34. P. D. Lax, “On the regularity of spectral densities,” Teor. Veroyat. i ee Primen.,8, No. 3, 337–340 (1963).

    Google Scholar 

  35. N. Levinson and H. McKean, “Weighted trigonometric approximations on R1 with application to the germ field of a stationary Gaussian noise,” Acta Math.,112, Nos. 1–2, 99–143 (1964).

    Google Scholar 

  36. Yu. A. Rozanov, “Some approximation problems in the theory of stationary processes,” J. Multivar. Anal.,2, No. 2, 135–144 (1972).

    Google Scholar 

  37. Yu. A. Rozanov, “Innovation processes and nonanticipative processes,” J. Multivar. Anal.,3, (1973).

  38. L. A. Shepp, “Radon-Nicodym derivatives of Gaussian measures,” Ann. Math. Statist.,37, No. 2, 321–354 (1966).

    Google Scholar 

  39. M. H. Stone, Linear Transformations in Hilbert Space, New York (1932).

  40. N. Wiener and P. Masani, “The prediction theory of multivariate stochastic processes. II. The linear predictor,” Acta Math,99, Nos. 1–2, 93–137 (May 1958).

    Google Scholar 

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  1. Yu. A. Rozanov
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Translated from Itogi Nauki i Tekhniki. Sovremennye Problemy Matematiki, Vol.3, pp. 181–258,1974.

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Rozanov, Y.A. Innovative processes and the factorization problem. J Math Sci 5, 397–450 (1976). https://doi.org/10.1007/BF01083781

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