{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T07:24:30Z","timestamp":1757575470015},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1978,12,1]],"date-time":"1978-12-01T00:00:00Z","timestamp":281318400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Systems Theory"],"published-print":{"date-parts":[[1978,12]]},"DOI":"10.1007\/bf01776572","type":"journal-article","created":{"date-parts":[[2005,6,18]],"date-time":"2005-06-18T06:29:16Z","timestamp":1119076156000},"page":"175-203","source":"Crossref","is-referenced-by-count":31,"title":["Basic optimal estimation and control problems in Hilbert space"],"prefix":"10.1007","volume":"12","author":[{"given":"R. M.","family":"DeSantis","sequence":"first","affiliation":[]},{"given":"R.","family":"Saeks","sequence":"additional","affiliation":[]},{"given":"L. J.","family":"Tung","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"BF01776572_CR1","volume-title":"Linear Optimal Control","author":"B. D. O. Anderson","year":"1971","unstructured":"B. D. O. Anderson, J. B. Moore,Linear Optimal Control, Prentice Hall, Englewood Cliffs, New Jersey, 1971."},{"key":"BF01776572_CR2","volume-title":"Control Theory of Systems Governed by Partial Differential Equations","author":"A. V. Balakrishnan","year":"1977","unstructured":"A. V. Balakrishnan, Stochastic Filtering and Control of Linear Systems: A General Theory,Control Theory of Systems Governed by Partial Differential Equations, Academic Press, New York, 1977."},{"key":"BF01776572_CR3","volume-title":"Applied Functional Analysis","author":"A. V. Balakrishnan","year":"1976","unstructured":"A. V. Balakrishnan,Applied Functional Analysis, Springer-Verlag, New York, 1976."},{"key":"BF01776572_CR4","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/S0022-0000(67)80028-X","volume":"1","author":"A. V. Balakrishnan","year":"1967","unstructured":"A. V. Balakrishnan, J. L. Lions, State Estimation for Infinite Dimensional Systems,J. Computer and Systems Sciences, 1, 391\u2013403, (1967).","journal-title":"J. Computer and Systems Sciences"},{"key":"BF01776572_CR5","unstructured":"J. F. Barrett, Construction of Linear Quadratic Regulators Using Spectral Factorization and the Return Difference Matrix,Techn. Report CN\/75\/4, The University of Cambridge, May 1975."},{"key":"BF01776572_CR6","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1109\/JRPROC.1950.231821","volume":"38","author":"H. W. Bode","year":"1950","unstructured":"H. W. Bode, C. E. Shannon, A Simplified Derivation of Linear Least Square Smoothing and Prediction Theory,Proc. IRE, 38, 417\u2013425, 1950.","journal-title":"Proc. IRE"},{"key":"BF01776572_CR7","volume-title":"Synthesis of Optimum Control Systems","author":"S. S. L. Chang","year":"1961","unstructured":"S. S. L. Chang,Synthesis of Optimum Control Systems, McGraw-Hill, New York, 1961."},{"key":"BF01776572_CR8","unstructured":"R. F. Curtain, Estimation and Stochastic Control for Linear Infinite Dimensional Systems,Probability Analysis and Related Topics, Vol 1, (Bhraucha-Reid Editor, Academic Press, New York (to appear)."},{"key":"BF01776572_CR9","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1109\/PROC.1976.10065","volume":"64","author":"R. M. DeSantis","year":"1976","unstructured":"R. M. DeSantis, Causality Theory in Systems Analysis,IEEE Proc., 64, 36\u201344, 1976.","journal-title":"IEEE Proc."},{"key":"BF01776572_CR10","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1016\/0022-247X(74)90148-6","volume":"48","author":"R. M. DeSantis","year":"1974","unstructured":"R. M. DeSantis, W. A. Porter, On the Generalization of the Volterra Principle of Inversion,J. Appl. Math. Anal., 48, 743\u2013748, 1974.","journal-title":"J. Appl. Math. Anal."},{"key":"BF01776572_CR11","unstructured":"R. M. DeSantis, Causality Structure of Engineering Systems,SEL Tech. Rep. 67, The University of Michigan, Ann Arbor, Michigan, Sept. 1972."},{"key":"BF01776572_CR12","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1137\/0124020","volume":"24","author":"R. M. DeSantis","year":"1973","unstructured":"R. M. DeSantis, W. A. Porter, On Time Related Properties of Non-linear Systems,SIAM J. Appl. Math., 24, 188\u2013206, 1973.","journal-title":"SIAM J. Appl. Math."},{"key":"BF01776572_CR13","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1090\/S0002-9939-1973-0317102-4","volume":"38","author":"R. M. DeSantis","year":"1973","unstructured":"R. M. DeSantis, On a Generalized Volterra Equation in Hilbert Space,Proc. AMS, 38, 563\u2013570, 1973.","journal-title":"Proc. AMS"},{"key":"BF01776572_CR14","unstructured":"D. Duttweiler, Reproducing Kernel Hilbert Space Techniques for Detection and Estimation Problems,Ph.D. Thesis, Stanford Univ., Stanford, 1970."},{"key":"BF01776572_CR15","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/S0019-9958(67)90417-2","volume":"11","author":"P. Falb","year":"1967","unstructured":"P. Falb, Infinite Dimensional Filtering: The Kalman-Bucy Filter in Hilbert Space,Information and Control, 11, 102\u2013137, 1967.","journal-title":"Information and Control"},{"key":"BF01776572_CR16","unstructured":"I. Z. Gohberg, M. G. Krein,Theory of Volterra Operators in Hilbert Space and Applications, (translation), Amer. Math. Soc., Providence, 1969."},{"key":"BF01776572_CR17","first-page":"102","volume":"5","author":"R. E. Kalman","year":"1960","unstructured":"R. E. Kalman, Contributions to the Theory of Optimal Control,Bol. Soc. Math. Mexicana, 5, 102\u2013119, 1960.","journal-title":"Bol. Soc. Math. Mexicana"},{"key":"BF01776572_CR18","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1115\/1.3658902","volume":"82","author":"R. E. Kalman","year":"1961","unstructured":"R. E. Kalman, R. S. Bucy, New Results in Linear Filtering and Prediction Theory, Trans. ASME, Series D.,J. of Basic Engrg., 82, 95\u2013100, 1961.","journal-title":"Trans. ASME, Series D., J. of Basic Engrg."},{"key":"BF01776572_CR19","doi-asserted-by":"crossref","unstructured":"T. Kailath, D. Duttweiler, A RKHS Approach to Detection and Estimation Problems\u2014Part III: Generalized Innovations Representations and a Likelihood Ratio Formula,IEEE Trans. on Infor. Theory, IT-18, 730\u2013745, 1972.","DOI":"10.1109\/TIT.1972.1054925"},{"key":"BF01776572_CR20","doi-asserted-by":"crossref","unstructured":"T. Kailath, An Innovation Approach to Least-Squares Estimation Parts I and II,IEEE Trans. on Auto. Contr., Vol. AC-13, No. 6, 646\u2013660, 1968.","DOI":"10.1109\/TAC.1968.1099019"},{"key":"BF01776572_CR21","volume-title":"Linear Optimal Control Systems","author":"H. Kwakernaak","year":"1972","unstructured":"H. Kwakernaak, R. Sivan,Linear Optimal Control Systems, Wiley-Interscience, New York, 1972."},{"key":"BF01776572_CR22","doi-asserted-by":"crossref","unstructured":"R. J. Leake, Duality Condition Established in the Frequency Domain,IEEE Trans. Infor. Theory, (correspondence), IT-11, 461, 1965.","DOI":"10.1109\/TIT.1965.1053786"},{"key":"BF01776572_CR23","first-page":"373","volume":"118","author":"A. G. J. MacFarlane","year":"1971","unstructured":"A. G. J. MacFarlane, Return Difference Matrix Properties for Optimal Stationary Kalman-Bucy Filter,Proc. IEEE, 118, 373\u2013376, 1971.","journal-title":"Proc. IEEE"},{"key":"BF01776572_CR24","volume-title":"Analytical Design of Linear Feedback Controls","author":"G. C. Newton","year":"1957","unstructured":"G. C. Newton, L. A. Gould, J. F. Kaiser,Analytical Design of Linear Feedback Controls, Wiley, New York, 1957."},{"key":"BF01776572_CR25","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/BF01691464","volume":"5","author":"W. A. Porter","year":"1971","unstructured":"W. A. Porter, A Basic Optimization Problem in Linear System,Math. Sys. Theory, 5, 20\u201344, 1971.","journal-title":"Math. Sys. Theory"},{"key":"BF01776572_CR26","volume-title":"Modern Foundations of Systems Theory","author":"W. A. Porter","year":"1966","unstructured":"W. A. Porter,Modern Foundations of Systems Theory, MacMillian, New York, 1966."},{"key":"BF01776572_CR27","unstructured":"W. A. Porter, C. L. Zahm, Basic Concepts in System Theory,SEL Tch. Rep. 33, The University of Michigan, Ann Arbor, Michigan, 1969."},{"key":"BF01776572_CR28","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1080\/00207177008931859","volume":"12","author":"W. A. Porter","year":"1970","unstructured":"W. A. Porter, Some Circuit Theory Concepts Revisited,Inter. J. of Contr., 12, 433\u2013448, 1970.","journal-title":"Inter. J. of Contr."},{"key":"BF01776572_CR29","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1080\/00207177108931968","volume":"13","author":"W. A. Porter","year":"1971","unstructured":"W. A. Porter, Nonlinear Systems in Hilbert Space,Inter. J. of Contr., 13, 593\u2013602, 1971.","journal-title":"Inter. J. of Contr."},{"key":"BF01776572_CR30","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/PROC.1976.10070","volume":"64","author":"R. Saeks","year":"1976","unstructured":"R. Saeks, The Factorization Problem\u2014A Survey,IEEE Proc., 64, 90\u201395, 1976.","journal-title":"IEEE Proc."},{"key":"BF01776572_CR31","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-80735-0","volume-title":"Resolution Space Operators and Systems","author":"R. Saeks","year":"1973","unstructured":"R. Saeks,Resolution Space Operators and Systems, Springer-Verlag, New York, 1973."},{"key":"BF01776572_CR32","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/0016-0032(76)90044-2","volume":"302","author":"R. Saeks","year":"1976","unstructured":"R. Saeks, Reproducing Kernel Resolution Space and Its Applications,J. of the Franklin Institute, 302, 331\u2013355, 1976.","journal-title":"J. of the Franklin Institute"},{"key":"BF01776572_CR33","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/B978-0-12-702450-9.50034-8","volume-title":"Vector and Operator Valued Measures","author":"R. Saeks","year":"1973","unstructured":"R. Saeks, Causal Factorization, Shift Operators and the Spectral Multiplicity Function,Vector and Operator Valued Measures, (D. H. Tucker, Ed.), Academic Press, New York, 319\u2013335, 1973."},{"key":"BF01776572_CR34","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1137\/1012080","volume":"12","author":"R. Saeks","year":"1970","unstructured":"R. Saeks, Causality in Hilbert Space,SIAM Rev., 12, 357\u2013383, 1970.","journal-title":"SIAM Rev."},{"key":"BF01776572_CR35","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1137\/1015030","volume":"15","author":"R. Saeks","year":"1973","unstructured":"R. Saeks, State in Hilbert Space,SIAM Rev., 15, 283\u2013308, 1973.","journal-title":"SIAM Rev."},{"key":"BF01776572_CR36","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1137\/1015074","volume":"15","author":"R. Saeks","year":"1973","unstructured":"R. Saeks, Fourier Analysis in Hilbert Space,SIAM Rev., 15, 604\u2013638, 1973.","journal-title":"SIAM Rev."},{"key":"BF01776572_CR37","unstructured":"A. Schumitzky, Unpublished Notes, Univ. of Southern California, 1978."},{"key":"BF01776572_CR38","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/S0022-0000(68)80005-4","volume":"2","author":"A. Schumitzky","year":"1968","unstructured":"A. Schumitzky, On the Equivalence Between Matrix Riccati Equations and Fredholm Resolvents,J. Comp. and Sys. Sciences, 2, 76\u201387, 1968.","journal-title":"J. Comp. and Sys. Sciences"},{"key":"BF01776572_CR39","unstructured":"W. K. Schnure, System Identification: A State Approach,SEL Tech. Rep. 80, Univ. of Michigan, Ann Arbor, Michigan, 1974."},{"key":"BF01776572_CR40","unstructured":"M. Steinberger, A. Schumitzky, and L. Silverman, Optimal Causal Feedback Control of Linear Infinite-Dimensional Systems,SIAM J. on Control, (to appear)."},{"key":"BF01776572_CR41","unstructured":"L. J. Tung, R. Saeks, Wiener-Hopf Techniques in Resolution Space,Proc. of the 2nd OTNS International Symposium, Texas Tech University, Aug. 1977."},{"key":"BF01776572_CR42","volume-title":"Wiener-Hopf Filtering and Control Formulated in Abstract Space","author":"L. J. Tung","year":"1977","unstructured":"L. J. Tung, Random Variables, Wiener-Hopf Filtering and Control Formulated in Abstract Space,Ph.D. Thesis, Texas Tech Univ., Lubbock, Texas, July 1977."},{"key":"BF01776572_CR43","volume-title":"Extrapolation, Interpolation and Smoothing of Stationary Time Series","author":"N. Wiener","year":"1966","unstructured":"N. Wiener,Extrapolation, Interpolation and Smoothing of Stationary Time Series, MIT Press, Cambridge, 1966."},{"key":"BF01776572_CR44","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1137\/0306023","volume":"6","author":"W. M. Wonham","year":"1968","unstructured":"W. M. Wonham, \u201cOn the Separation Theorem of Stochastic Control,\u201dSIAM J. Control, 6, 312\u2013326, 1968.","journal-title":"SIAM J. Control"},{"key":"BF01776572_CR45","doi-asserted-by":"crossref","unstructured":"D. C. Youla, H. A. Jabr, J. J. Bongiorno, Modern Wiener-Hopf Design of Optimal Controllers, Parts I and II,IEEE Trans. on Automatic Control, AC-21, 3\u201313, 319\u2013337, 1976.","DOI":"10.1109\/TAC.1976.1101223"}],"container-title":["Mathematical Systems Theory"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01776572.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01776572\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01776572","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,7]],"date-time":"2020-04-07T20:45:57Z","timestamp":1586292357000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01776572"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,12]]},"references-count":45,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1978,12]]}},"alternative-id":["BF01776572"],"URL":"https:\/\/doi.org\/10.1007\/bf01776572","relation":{},"ISSN":["0025-5661","1433-0490"],"issn-type":[{"value":"0025-5661","type":"print"},{"value":"1433-0490","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,12]]}}}