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Controllability of Laguerre and Jacobi equations. (English) Zbl 1133.93007

Summary: We study the controllability of the controlled Laguerre equation and the controlled Jacobi equation. For each case, we find conditions which guarantee when such systems are approximately controllable on the interval \([0, t_{1}]\). Moreover, we show that these systems can never be exactly controllable.

MSC:

93B05 Controllability
93C20 Control/observation systems governed by partial differential equations
93C05 Linear systems in control theory
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[1] Balderrama C, Fractional integration and fractional differentiation for d-dimensional Jacobi expansions · Zbl 1198.42024
[2] Barcenas D, IMA J. Math. Contr. Inform. 22 pp 310– (2005) · Zbl 1108.93014
[3] Barcenas D, IMA J. Math. Contr. Inform. 23 pp 1– (2006) · Zbl 1106.93007
[4] DOI: 10.1007/BF01180560 · JFM 55.0260.01
[5] Bochner S, Proceedings of the Conference on Differential Equations pp 23– (1955)
[6] DOI: 10.2307/1911242 · Zbl 1274.91447
[7] Curtain RF, Lecture Notes in Control and Information Sciences 8 (1978)
[8] Curtain RF, Text in Applied Mathematics 21 (1995)
[9] DOI: 10.1137/0304048 · Zbl 0168.34906
[10] DOI: 10.1016/0022-0396(67)90039-3 · Zbl 0155.15903
[11] Graczyk P, J. Math. Pures Appl. 84 pp 375– (2005) · Zbl 1129.42015
[12] Imanuvilov OY, Proceedings of International Congress of Mathematicians pp 1321– (2006)
[13] Krall HL, Duke Math. J. 4 pp 705– (1938) · Zbl 0020.02002
[14] Krall HL, The Pennsylvania Sate College Studies, no. 6 (1940)
[15] DOI: 10.1090/S0002-9947-1949-0028473-1
[16] Liouville J, Journal de Mathématiques Pures et Appliquées 2 pp 16– (1837)
[17] Meyer PA, Theory and Applications of Random Fields pp 201– (1983)
[18] Miranian L, J. Phys. A: Math. Gen. 38 pp 6379– (2005) · Zbl 1076.33007
[19] Muckenhoupt B, Trans. Amer. Math. Soc. 139 pp 231– (1969)
[20] Naylor A, Linear Operator Theory in Engineering and Science (1971)
[21] Russell DL, SIAM Rev. 20 pp 636– (1978) · Zbl 0397.93001
[22] Sturm CF, Journal de Mathématiques Pures et Appliquées 1 pp 106– (1836)
[23] Szego G, Amer. Math. Soc. Colloq. Publ., Rev. ed. 23 (1959)
[24] Torrea JL, Margarita Mathematica (2001)
[25] DOI: 10.1137/0314022 · Zbl 0326.93003
[26] Young N, An Introduction to Hilbert Spaces (1995)
[27] Zuazua E, Proceedings of International Congress of Mathematicians pp 1389– (2006)
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