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Operator factorization on partially ordered Hilbert resolution spaces. (English) Zbl 0505.93043


MSC:

93C25 Control/observation systems in abstract spaces
47A65 Structure theory of linear operators
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
06A06 Partial orders, general
46C99 Inner product spaces and their generalizations, Hilbert spaces
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References:

[1] Proceedings of the IEEE,Special Issue on Multidimensional Systems (Ed. Bose) (June 1977)
[2] DeSantis, R. M., Saeks, R., and Tung, L. Basic Optimal Estimation and Control Problems in Hilbert Space,Math. Systems Theory, vol. 12, pp. 175–203 (1978) · Zbl 0386.93055 · doi:10.1007/BF01776572
[3] DeSantis, R. M., and Porter, W. A. Optimization Problems in Partially Ordered Hilbert Resolution Spaces,Int. J. Control, 1982 · Zbl 0515.93070
[4] Feintuch, A., Saeks, R.System Theory: A Hilbert Space Approach. Academic Press (1981) · Zbl 0488.93003
[5] Gohberg, I. Z., Krein, M. G.,Theory and Application of Volterra Operators in Hilbert Space (translation) AMS, vol. 4 (1970) · Zbl 0194.43804
[6] Porter, W. A., On Factoring the Polyvariance Operator,Math. System Theory, vol. 13, 4 (1981) · Zbl 0456.93059
[7] Porter, W. A., DeSantis, R. M., Angular Factorization of Matrices, to appear,Math. Analysis and Applications (1982) · Zbl 0488.15009
[8] Saeks, R.Resolution Space Operators and Systems. New York: Springer-Verlag, 1973. · Zbl 0259.49001
[9] Special Mini-Issue on Image Processing,IEEE Transactions on Automatic Control (October 1978)
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