On the generators of non-negative contraction semi-groups in Banach lattices

Ken-iti SATO

doi:10.2969/jmsj/02030423

Ken-iti SATO

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ジャーナルフリー

1968 年 20 巻 3 号 p. 423-436

DOI https://doi.org/10.2969/jmsj/02030423

詳細

Published: 1968 Received: 1967/09/01 Available on J-STAGE: 2006/09/26 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/26 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) S. Bochner, Harmonic analysis and the theory of probability, Univ. Calif. Press, Berkeley-Los Angeles, 1955.
2) N. Dunford and J. T. Schwartz, Linear operators, Part I, Interscience, New York, 1958.
3) M. Hasegawa, On contraction semi-group and (di)-operators, J. Math. Soc. Japan, 18 (1966), 290-302.
4) P.-A. Meyer, Probabilité et potentiel, Hermann, Paris, 1966.
5) E. Nelson, Feynman integrals and the Schrödinger equation, J. Math. and Phys., 5 (1964), 332-343.
6) R. S. Phillips, On the generation of semigroups of linear operators, Pacific J. Math., 2 (1952), 343-369.
7) R. S. Phillips, Semi-groups of positive contraction operators, Czechoslovak Math. J., 12 (87) (1962), 294-313.
8) K. Sato and T. Ueno, Multi-dimensional diffusion and the Markov process on the boundary, J. Math. Kyoto Univ., 4 (1965), 529-605.
9) H. Trotter, On the product of semi-groups of operators, Proc. Amer. Math. Soc., 10 (1959), 545-551.
10) A. D. Ventcel', On lateral conditions for multi-dimensional diffusion processes, Teor. Verojatnost. i Primenen., 4 (1959), 172-185 (Russian).
11) K. Yosida, Functional analysis, Springer, Berlin-Heidelberg-New York, 1965.
12) K. Yosida, A perturbation theorem for semi-groups of linear operators, Proc. Japan Acad., 41 (1965), 645-647.
13) K. Yosida, Positive resolvents and potentials (an operator-theoretical treatment of Hunt's theory of potentials), Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 8 (1967), 210-218.

Right : [1] S. Bochner, Harmonic analysis and the theory of probability, Univ. Calif. Press, Berkeley-Los Angeles, 1955.
[2] N. Dunford and J. T. Schwartz, Linear operators, Part I, Interscience, New York, 1958.
[3] M. Hasegawa, On contraction semi-group and (di)-operators, J. Math. Soc. Japan, 18 (1966), 290-302.
[4] P. -A. Meyer, Probabilité et potentiel, Hermann, Paris, 1966.
[5] E. Nelson, Feynman integrals and the Schrödinger equation, J. Math. and Phys., 5 (1964), 332-343.
[6] R. S. Phillips, On the generation of semigroups of linear operators, Pacific J. Math., 2 (1952), 343-369.
[7] R. S. Phillips, Semi-groups of positive contraction operators, Czechoslovak Math. J., 12 (87) (1962), 294-313.
[8] K. Sato and T. Ueno, Multi-dimensional diffusion and the Markov process on the boundary, J. Math. Kyoto Univ., 4 (1965), 529-605.
[9] H. Trotter, On the product of semi-groups of operators, Proc. Amer. Math. Soc., 10 (1959), 545-551.
[10] A. D. Ventcel', On lateral conditions for multi-dimensional diffusion processes, Teor. Verojatnost. i Primenen., 4 (1959), 172-185 (Russian).
[11] K. Yosida, Functional analysis, Springer, Berlin-Heidelberg-New York, 1965.
[12] K. Yosida, A perturbation theorem for semi-groups of linear operators, Proc. Japan Acad., 41 (1965), 645-647.
[13] K. Yosida, Positive resolvents and potentials (an operator-theoretical treatment of Hunt's theory of potentials), Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 8 (1967), 210-218.

訂正日: 2006/09/26 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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