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

Seizô ITÔ

doi:10.2969/jmsj/01640307

Seizô ITÔ

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JOURNAL FREE ACCESS

1964 Volume 16 Issue 4 Pages 307-334

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

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Published: 1964 Received: June 27, 1964 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 26, 2006 Reason for correction: - Correction: TITLE Details: 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

Date of correction: September 26, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Seizo ITO¹⁾
Right : Seizô ITÔ¹⁾

Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: 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.

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