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Optimal control in Banach spaces. (English) Zbl 0155.15902


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[1] Fattorini, H. O., Time-optimal control of solutions of operational differential equations, J. SIAM Control, Ser. A, 2, 54-59 (1964) · Zbl 0143.16803
[2] Balakrishnan, A. V., Optimal control problems in Banach spaces, J. SIAM Control, Ser. A, 3, 152-180 (1965) · Zbl 0178.44601
[3] Falb, P. L., Infinite dimensional control problems I: On the closure of the set of attainable states for linear systems, J. Math. Analys. Appl., 9, 12-22 (1964) · Zbl 0128.10102
[4] J. L. Lions; J. L. Lions
[5] J. L. Lions; J. L. Lions · Zbl 0151.15003
[6] Pontryagin, L. S.; Boltyanskii, V. G.; Gamkrelidze, R. V.; Mishchenko, E. F., The Mathematical Theory of Optimal Processes (1962), Wiley (Interscience): Wiley (Interscience) New York · Zbl 0102.32001
[7] Egorov, A. I., On optimal control of processes in distributed objects, J. Appl. Math. Mech., 27, 1045-1058 (1963) · Zbl 0133.05601
[8] Egorov, A. I., On a variational problem in the theory of equations of elliptic type, Sibirski Math. J., 5, 500-508 (1964) · Zbl 0124.05401
[9] Egorov, Yu. V., Sufficient conditions for optimal control in Banach space, Math. Sbornik, 64, 106, 79-101 (1964) · Zbl 0196.47301
[10] Tanabe, H., A class of the equations of evolution in a Banach space, Osaka Math. J., 11, 121-145 (1959) · Zbl 0098.31201
[11] Tanabe, H., Remarks on the equations of evolution in a Banach space, Osaka Math. J., 12, 145-166 (1960) · Zbl 0098.31202
[12] Tanabe, H., On the equations of evolution in a Banach space, Osaka Math. J., 12, 363-376 (1960) · Zbl 0098.31301
[13] Sobolevski, P. E., On equations of parabolic type in a Banach space, (Trudy Moscov. Math. Občš., 10 (1961)), 297-350
[14] Yoshida, K., Functional Analysis (1965), Springer-Verlag: Springer-Verlag Berlin
[15] Natanson, I. P., The Theory of Functions of a Real Variable (1955), Ungar: Ungar New York · Zbl 0064.29102
[16] Lees, M.; Protter, M. H., Unique continuation for parabolic differential equations and inequalities, Duke Math. J., 28, 369-382 (1961) · Zbl 0143.33301
[17] Lions, J. L.; Malgrange, B., Sur l’unicité rétrograde dans les problèmes mixtes paraboliques, Math. Scand., 8, 277-286 (1960) · Zbl 0126.12202
[18] Agmon, S.; Nirenberg, L., Properties of solutions of ordinary differential equations in Banach space, Comm. Pure Appl. Math., 16, 121-239 (1963) · Zbl 0117.10001
[19] Komatzu, H., Abstract analyticity in time and unique continuation property for solutions of parabolic equations, J. Fac. Sci. Univ. Tokyo, 9, 1-11 (1961), Sec. I
[20] Friedman, A., Differentiability of solutions of ordinary differential equations in Hilbert space, Pacific J. Math., 16, 267-271 (1966) · Zbl 0151.20303
[21] Friedman, A.; Shinbrot, M., Volterra integral equations in Banach space, Trans. Amer. Math. Soc. (1967), to appear · Zbl 0147.12302
[22] Dunford, N.; Schwartz, J. T., Linear Operators, Part I: General Theory (1958), Wiley (Interscience): Wiley (Interscience) New York
[23] Mazur, S., Über konvexe Mengen in linearen normierten Räumen, Studia Math., 4, 70-84 (1933) · JFM 59.1074.01
[24] Klee, V. L., The support of a convex set in a linear normed space, Duke Math. J., 15, 767-772 (1948) · Zbl 0031.21804
[25] Agmon, S., On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math., 15, 119-147 (1962) · Zbl 0109.32701
[26] Hille, E.; Phillips, R. S., Functional Analysis and Semigroups (1957), American Mathematical Society Colloquium Publications: American Mathematical Society Colloquium Publications Providence, Rhode Island · Zbl 0078.10004
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