Article PDF
Avoid common mistakes on your manuscript.
Literature Cited
I. M. Gel'fand and A. M. Yaglom, "Computation of the amount of information about a stochastic function contained in another such function," Usp. Mat. Nauk,12, No. 1, 3–52 (1957).
M. S. Pinsker, "The extrapolation of random vector process and the quantity of information contained in a stationary random vector process relative to another one stationarily connected with it," Dokl. Akad. Nauk SSSR,121, No. 1, 49–51 (1958).
J. Chover, "On normalized entropy and the extensions of a positive-definite function," J. Math. Mech.,10, No. 6, 927–945 (1961).
Yu. A. Rozanov, "Spectral theory of n-dimensional stationary stochastic processes with discrete time," Usp. Mat. Nauk,13, No. 2, 93–142 (1958).
D. Z. Arov, "Realization of a canonical system with a dissipative boundary condition at one end of the segment in terms of the coefficient of dynamical compliance," Sib. Mat. Zh.,16, No. 3, 440–463 (1975).
M. G. Krein and A. A. Nudel'man, The Markov Problem of Moments and Extremal Problems [in Russian], Nauka, Moscow (1973).
I. V. Kovalishina, "J-Expansive matrix-valued functions in the Caratheodory problem," Dokl. Akad. Nauk Arm. SSR,9, No. 3, 129–135 (1974).
G. M. Il'mushkin, Candidate's Dissertation, Ul'yanovsk (1974).
J. P. Burg, Ph. D. Thesis, Department of Geophysics, Stanford Univ. (1975).
S. Haykin (editor), Nonlinear Methods of Spectral Analysis, Springer-Verlag, Berlin (1979).
H. Dym and I. Gokhberg, "Integral equations and operator theory,"2, No. 4, 503–528 (1979).
G. Szegö, Orthogonal Polynomials, Revised Edition, Amer. Math. Soc., Providence, Rhode Island (1958).
M. G. Krein, Dokl. Akad. Nauk SSSR,26, No. 1, 17–22 (1940).
M. G. Krein, Dokl. Akad. Nauk SSSR,44, No. 5, 191–195 (1944).
H. Dym and H. P. McKean, Gaussian Processes, Function Theory, and the Inverse Spectral Problem, Academic Press, New York (1976).
H. Dym and I. Gokhberg, "Integral Equations and Operator Theory,"3, No. 2, 142–215 (1980).
V. M. Adamyan, D. Z. Arov, and M. G. Krein, "Infinite Hankel block matrices and related problems of extensions," Izv. Akad. Nauk Arm. SSR,6, Nos. 2–3, 87–112 (1971).
Additional information
K. D. Ushinskii Odessa State Pedagogical Institute. Physicochemical Institute, Academy of Sciences of the Ukrainian SSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 15, No. 2, pp. 61–64, April–June, 1981.
Rights and permissions
About this article
Cite this article
Arov, D.Z., Krein, M.G. Problem of search of the minimum of entropy in indeterminate extension problems. Funct Anal Its Appl 15, 123–126 (1981). https://doi.org/10.1007/BF01082283
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01082283