Abstract
In this paper it is shown that the maximum entropy principle, which identifies the band extension on the real line, may be derived from the corresponding result for operator functions on the unit circle.
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References
D.Z. Arov and M.G. Krein, Problems of search of the minimum of entropy in indeterminate extension problems, Funct. Anal. Appl. 15 (1981), 123–126.
M.A. Barkar and I.C. Gohberg, On factorizations of operators relative to a discrete chain of projectors in Banach spaces, Amer. Math. Soc. Transl. (2) 90 (1970), 81–103. [Mat Issled. 1 (1966), 32–54, Russian.]
H. Bart, I. Gohberg and M. A. Kaashoek, Minimal factorization of matrix and operator functions, OT 1, Birkhäuser Verlag, Basel, 1979.
J.J. Benedetto, A quantitative maximum entropy theorem for the real line, Integral Equations and Operator Theory 10 (1987), 761–779.
J. Chover, On normalized entropy and the extensions of a positive definite function, J. Math. Mech. 10 (1961), 927–945.
H. Dym, J Contractive matrix functions, reproducing kernel Hilbert spaces and interpolation, CBMS 71, Amer. Math. Soc, Providence, RI, 1989.
H. Dym and I. Gohberg, On an extension problem, generalized Fourier analysis and an entropy formula, Integral Equations and Operator Theory 3 (1980), 143–215.
I. Gohberg, S. Goldberg and M.A. Kaashoek, Classes of Linear Operators, Volume I, Birkhäuser Verlag, Basel, 1990.
I. Gohberg and M.A. Kaashoek, Asymptotic formulas of Szegö-Kac-Achiezer type, Asymptotic Analysis, to appear.
I. Gohberg and M.A. Kaashoek, The band extension of the real line as a limit of discrete band extensions, I. The main limit theorem, Proceedings Workshop on Operator Theory and Complex Analysis, Sapporo, Japan, 1991, to appear.
I. Gohberg, M.A. Kaashoek and H.J. Woerdeman, The band method for positive and contractive extension problems, J. Operator Theory 22 (1989), 109–155.
I. Gohberg, M.A. Kaashoek and H.J. Woerdeman, The band method for positive and contractive extension problems: An alternative version and new applications, Integral Equations and Operator Theory 12 (1989), 343–382.
I. Gohberg, M.A. Kaashoek and H.J. Woerdeman, A maximum entropy principle in the general framework of the band method, J. Funct. Anal. 95 (1991), 231–254.
I.C. Gohberg and M.G. Krein, Introduction to the theory of nonselfadjoint operators, Transi. Math. Monographs 18, Amer. Math. Soc, Providence, RI, 1969.
L.A. Ljusternik and W.I. Sobolev, Elemente der Funktionalaysis, Akademie-Verlag, Berlin, 1960.
D. Mustafa and K. Glover, Minimum entropy H ∞ control, Lecture Notes in Control and Information Sciences 146, Springer Verlag, Berlin, 1990.
A. Perelson, Generalized traces and determinants for compact operators, Ph.D. Thesis, Tel-Aviv University, 1987.
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© 1992 Springer Basel AG
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Gohberg, I., Kaashoek, M.A. (1992). The Band Extension on the Real Line as a Limit of Discrete Band Extensions, II. The Entropy Principle. In: Gohberg, I. (eds) Continuous and Discrete Fourier Transforms, Extension Problems and Wiener-Hopf Equations. Operator Theory: Advances and Applications, vol 58. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8596-6_3
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DOI: https://doi.org/10.1007/978-3-0348-8596-6_3
Publisher Name: Birkhäuser, Basel
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