The global hypoellipticity of degenerate elliptic-parabolic operators

Kazuo AMANO

doi:10.2969/jmsj/04020181

Kazuo AMANO

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ジャーナルフリー

1988 年 40 巻 2 号 p. 181-204

DOI https://doi.org/10.2969/jmsj/04020181

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Published: 1988 Received: 1985/06/12 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) K. Amano, The global hypoellipticity of a class of degenerate elliptic-parabolic operators, Proc. Japan Acad., 60 (1984), 312-314.
2) K. Amano, Stochastic representation and singularities of solutions of second order equations with semidefinite characteristic form, Trans. Amer. Math. Soc., 286 (1984), 295-312.
3) V.S. Fedii, On a criterion for hypoellipticity, Math. USSR-Sb., 14 (1971), 15-45.
4) V.S. Fedii, An example of a second order nonhypoelliptic operator with the property of global hypoellipticity, Mat. Zametki, 12 (1972), 269-274.
5) C. Fefferman and D. H. Phong, Subelliptic eigenvalue problems, Proc. Conf. on Harmonic Analysis, in honor of Antoni Zygmund, Wadworth Math. Series, 1981, pp. 590-606.
6) D. Fujiwara and H. Omori, An example of a globally hypo-elliptic operator, Hokkaido Math. J., 12 (1983), 293-297.
7) S. J. Greenfield and N. Wallach, Global hypoellipticity and Liouville numbers, Proc. Amer. Math. Soc., 31 (1972), 112-114.
8) L. Hörmander, Pseudo-differential operators and hypoelliptic equations, Proc. Symposium on Singular Integrals, Amer. Math. Soc., 10 (1967), 138-183.
9) L. Hörmander, Hypoelliptic second order differential equations, Acta Math., 119 (1967), 147-171.
10) H. Kumano-go, Pseudo-differential Operators, MIT Press, Cambridge, 1981
11) S. Kusuoka, Malliavin calculus and its applications, Sûgaku, 36 (1984), 97-109 (in Japanese).
12) S. Kusuoka and D. W. Stroock, Applications of the Malliavin calculus III, to appear.
13) Y. Morimoto, On the hypoellipticity for infinitely degenerate semi-elliptic operators, J. Math. Soc. Japan, 30 (1978), 327-358.
14) O. A. Oleinik and E. V. Radkevich, Second order equations with nonnegative characteristic form, Amer. Math., Soc., Providence, Rhode Island and Plenum Press, 1973.
15) H. Omori, On global hypoellipticity of covariant Laplacians on principal bundles, to appear.
16) D.W. Stroock and S.R.S. Varadhan, On degenerate elliptic-parabolic operators of second order and their associated diffusions, Comm. Pure Appl. Math., 25 (1972), 651-713.
17) K. Taira, Le principe du maximum et l'hypoellipticité globale, Séminaire Bony-Sjöstrand-Meyer, 1984-1985, Expose no. I.

Right : [1] K. Amano, The global hypoellipticity of a class of degenerate elliptic-parabolic operators, Proc. Japan Acad., 60 (1984), 312-314.
[2] K. Amano, Stochastic representation and singularities of solutions of second order equations with semidefinite characteristic form, Trans. Amer. Math. Soc., 286 (1984), 295-312.
[3] V. S. Fedii, On a criterion for hypoellipticity, Math. USSR-Sb., 14 (1971), 15-45.
[4] V. S. Fedii, An example of a second order nonhypoelliptic operator with the property of global hypoellipticity, Mat. Zametki, 12 (1972), 269-274.
[5] C. Fefferman and D. H. Phong, Subelliptic eigenvalue problems, Proc. Conf. on Harmonic Analysis, in honor of Antoni Zygmund, Wadworth Math. Series, 1981, pp. 590-606.
[6] D. Fujiwara and H. Omori, An example of a globally hypo-elliptic operator, Hokkaido Math. J., 12 (1983), 293-297.
[7] S. J. Greenfield and N. Wallach, Global hypoellipticity and Liouville numbers, Proc. Amer. Math. Soc., 31 (1972), 112-114.
[8] L. Hörmander, Pseudo-differential operators and hypoelliptic equations, Proc. Symposium on Singular Integrals, Amer. Math. Soc., 10 (1967), 138-183.
[9] L. Hörmander, Hypoelliptic second order differential equations, Acta Math., 119 (1967), 147-171.
[10] H. Kumano-go, Pseudo-differential Operators, MIT Press, Cambridge, 1981
[11] S. Kusuoka, Malliavin calculus and its applications, Sûgaku, 36 (1984), 97-109 (in Japanese).
[12] S. Kusuoka and D. W. Stroock, Applications of the Malliavin calculus III, to appear.
[13] Y. Morimoto, On the hypoellipticity for infinitely degenerate semi-elliptic operators, J. Math. Soc. Japan, 30 (1978), 327-358.
[14] O. A. Oleinik and E. V. Radkevich, Second order equations with nonnegative characteristic form, Amer. Math., Soc., Providence, Rhode Island and Plenum Press, 1973.
[15] H. Omori, On global hypoellipticity of covariant Laplacians on principal bundles, to appear.
[16] D. W. Stroock and S. R. S. Varadhan, On degenerate elliptic-parabolic operators of second order and their associated diffusions, Comm. Pure Appl. Math., 25 (1972), 651-713.
[17] K. Taira, Le principe du maximum et l'hypoellipticité globale, Séminaire Bony-Sjöstrand-Meyer, 1984-1985, Expose no. I.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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