�� , �� -�� (original) (raw)

�� , �� , �� , �� .

�� , �� 1940 �. (��. [1]–[5]), �� , �� . �� , �� , �� .

�� . �� , �� , �� -�� , �� (��., � ��, �� . �. �� [2] � [20]). �� . �� , �� 1966 �. � �� (��. [18]).

�� , �� , �� (��., � ��, [10], [12]). �� , �� 2005 �. � �� [24].

�� , �� . � �� ��. �� — ��. �� , �� . �� (� �� ) �� . �. �� (��. [6], [7]). �� . �. �� (��. [8]). �� ��.

�� . �. �� . �. ��, �� 1954 �. (��. [9]). � �� , �� . � ��, �� . �� 1969 �. (��. [11]).

�� «��-��» �� . �� , �� .

�� -�� , �� «��-��» ��. �� , �� e, � �� «��-��» �� [15, p. 47]. �� ., ��, [14], [16], [17],[19],[21].

� �� , �� [23]. � �� . [22]. �� ., � ��, [13].

��

[1]�� . �.,� �� -��. I//��. �� , ��. ��., 4, 465–478 (1940).

[2]�� . �., � �� -��. II// ��. �� , ��. ��., 1946, 10, 277–279 (1946).

[3]�� . �., � �� -��. III (�� .�.��) // �� , ��. 12, 165–168 (1964).

[4]�� . �., � �� -��// �� , ��. 12, 169–179 (1964).

[5]�� . �., �� . �: ��, 1979.

[6]�� . �., �� -��// ��. ��. ��. ��. ��-��, 16, ��.-��. �-�, 3, 97–126 (1951).

[7]�� . �., �� -��.// ��. �� , 76, 801–804 (1951).

[8]�� . �., � �� -��// ��. ��., 34(76), 407–416, (1954).

[9]�� .�., �� .�., � �� , �� -�� // ��. ��, 2, 45–65 (1954).

[10]Artstein Z. “Yet another proof of the Lyapunov convexity theorem,” Proc. Amer. Math. Soc., 108:1, 89–91 (1990).

[11]Bolker E., “A class of convex bodies,” Trans. Amer. Math. Soc., 145, 323–345 (1969)

[12]Elton J., Hill Th. “A generalization of Lyapounov's convexity theorem to measures with atoms,” Proc. Amer. Math. Soc., 99:2, 297–304 (1987).

[13]Goodey P., Weil W., “Zonoids and generalisations,” In: �andbook of Convex Geometry, Vol. �., North-Holland, Amsterdam etc., 1296–1326 (1993).

[14]Halkin H., “A generalization of LaSalle’s bang-bang principle,” SIAM Journal on Control and Optimization, 2, 199–202 (1965).

[15]Hermes H., LaSalle J. P.,Functional Analysis and Time Optimal Control. Academic Press, New York–London, 1969.

[16]LaSalle J. P., “The time optimal control problem,” In: Contributions to the Theory of Non-Linear Oscillations, Vol. 5, Ann. Math. Studies 45, 1–24, Princeton Univ. Press, 1960.

[17]Levinson N., “Minimax, Liapunov, and ‘bang-bang,’” J. Diff. Equat. 2, 218–241 (1966).

[18]Lindenstrauss J., “A short proof of Liapounoff’s convexity theorem,” J. Math. Mech.,15, 971–972 (1966).

[19]Neustadt L. W., “The existence of optimal control in the absence of convexity,” J. Math. Anal. Appl., 7, 110–117 (1963).

[20]Nunke R. J., Savage L. J., “On the set of values of a nonatomic, finitely additive, finite measure,” Proc. Amer. Math. Soc., 3:2, 217–218 (1952).

[21]Olech C. “Extremal solutions of a control system,” J. Diff. Eq., 2, 74–101 (1966).

[22]Pap E. (Ed.)Handbook of Measure Theory. Vol. 1 and 2. North Holland, Amsterdam (2002).

[23]Pietsch A.,_History of Banach Spaces and Linear Operators._Birkhäuser, Boston etc. (2007).

[24]Ross D., “An elementary proof of Lyapunov’s theorem,” Amer. Math.Monthly112:7, 651–653 (2005).

������� ��������, ������� � ����-���� (original) (raw)

����������

�� , �� -�� (original) (raw)

��