Martin boundary for linear elliptic differential operators of second order in a manifold

Seizô ITÔ

doi:10.2969/jmsj/01640307

Seizô ITÔ

著者情報

ジャーナルフリー

1964 年 16 巻 4 号 p. 307-334

DOI https://doi.org/10.2969/jmsj/01640307

詳細

Published: 1964 Received: 1964/06/27 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: 論文タイトル訂正内容: Wrong : Martin boundary for liner elliptic differential operators of second order in a manifold
Right : Martin boundary for linear elliptic differential operators of second order in a manifold

訂正日: 2006/09/26 訂正理由: - 訂正箇所: 著者情報訂正内容: Wrong : Seizo ITO¹⁾
Right : Seizô ITÔ¹⁾

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) N. Aronszajn, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, Tech. Report 16, Univ. of Kansas (1956).
2) M. Brelot, Lectures on potential theory, Tata Inst. of Fundamental Research, Bombay, 1960.
3) J. L. Doob, Discrete potential theory and boundaries, J. Math. Mech., 8 (1959,) 433-458.
4) G. A. Hunt, Markov chains and Martin boundaries, Ill, J. Math., 4 (1960), 313-340.
5) S. Ito, A boundary value problem of partial differential equations of parabolic type, Duke Math. J., 24 (1957), 299-312.
6) S. Ito, Fundamental solutions of parabolic differential equations and boundary value problems, Japan. J. Math., 27 (1957), 55-102.
7) S. Ito, On existence of Green function and positive superharmonic functions for linear elliptic operators of second order, this volume, 299-306.
8) R. S. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc., 49 (1941), 137-172.
9) M. G. šur, Martin's boundary for linear elliptic operators of second order, Izv. Akad. Nauk, SSSR., 27 (1963), 45-60 (Russian).
10) T. Watanabe, On the theory of Martin boundaries induced by countable Markov processes, Mem. Coll. Sci. Univ. Kyoto Ser. A, 33 (1960), 39-108.

Right : [1] N. Aronszajn, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, Tech. Report 16, Univ. of Kansas (1956).
[2] M. Brelot, Lectures on potential theory, Tata Inst. of Fundamental Research, Bombay, 1960.
[3] J. L. Doob, Discrete potential theory and boundaries, J. Math. Mech., 8 (1959,) 433-458.
[4] G. A. Hunt, Markov chains and Martin boundaries, Ill, J. Math., 4 (1960), 313-340.
[5] S. Itô, A boundary value problem of partial differential equations of parabolic type, Duke Math. J., 24 (1957), 299-312.
[6] S. Itô, Fundamental solutions of parabolic differential equations and boundary value problems, Japan. J. Math., 27 (1957), 55-102.
[7] S. Itô, On existence of Green function and positive superharmonic functions for linear elliptic operators of second order, this volume, 299-306.
[8] R. S. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc., 49 (1941), 137-172.
[9] M. G. Šur, Martin's boundary for linear elliptic operators of second order, Izv. Akad. Nauk, SSSR., 27 (1963), 45-60 (Russian).
10) T. Watanabe, On the theory of Martin boundaries induced by countable Markov processes, Mem. Coll. Sci. Univ. Kyoto Ser. A, 33 (1960), 39-108.

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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