Asymptotic behavior of spectral functions of elliptic operators with Hölder continuous coefficients

Yoichi MIYAZAKI

doi:10.2969/jmsj/04930539

Yoichi MIYAZAKI

著者情報

ジャーナルフリー

1997 年 49 巻 3 号 p. 539-563

DOI https://doi.org/10.2969/jmsj/04930539

詳細

Published: 1997 Received: 1995/06/22 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) S. Agmon, On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems, Comm. Pure Appl. Math., 18 (1965), 627-663.
2) S. Agmon, Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators, Arch. Rational Mech. Anal., 28 (1968), 165-183.
3) R. Beals, Asymptotic behavior of the Green's function and spectral function of an elliptic operator, J. Funct. Anal., 5 (1970), 484-503.
4) J. Brüning, Zur abschatzung der spektral-function elliptisher operatoren, Math. Z., 137 (1974), 75-85.
5) S. D. Eidel'man, Parabolic Systems, North-Holland, Amsterdam, 1969.
6) K. Maruo and H. Tanabe, On the asymptotic distribution of eigenvalues of operators associated with strongly elliptic sesquilinear forms, Osaka J. Math., 8 (1971), 323-345.
7) K. Maruo, Asymptotic distribution of eigenvalues of non-symmetric operators associated with strongly elliptic sesquilinear forms, Osaka J. Math., 9 (1972), 547-560.
8) G. Métivier, Estimation du reste en theorie spectrale, in Seminar Analysis 1982/1983, Inst. Math., Berlin (1983), 70-96.
9) Y. Miyazaki, A sharp asymptotic remainder estimate for the eigenvalues of operators associated with strongly elliptic sesquilinear forms, Japan. J. Math., 15 (1989), 65-97.
10) Y. Miyazaki, The eigenvalue distribution of elliptic operators with Hölder continuous coefficients, Osaka J. Math., 28 (1991), 935-973.
11) Y. Miyazaki, The eigenvalue distribution of elliptic operators with Hölder continuous coefficients II, Osaka J. Math., 30 (1993), 267-301.
12) T. Muramatu, Interpolation Theory and Linear Operators, Iwanami, Tokyo, in Japanese, 1985.
13) E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, New Jersey, 1970.
14) H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North Holland Publ., Amsterdam-New York, 1978.
15) J. Tsujimoto, On the remainder estimates of asymptotic formula for eigenvalues of operators associated with strongly elliptic sesquilinear forms, J. Math. Soc. Japan, 33 (1981), 557-569.
16) J. Tsujimoto, On the asymptotic behavior of spectral functions of elliptic operators, Japan. J. Math., 8 (1982), 177-210.
17) J. Tsujimoto, Asymptotic estimates for spectral functions of elliptic operators and its application, RIMS, Kôkyûroku 530, 17-23, in Japanese, 1984.

Right : [1] S. Agmon, On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems, Comm. Pure Appl. Math., 18 (1965), 627-663.
[2] S. Agmon, Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators, Arch. Rational Mech. Anal., 28 (1968), 165-183.
[3] R. Beals, Asymptotic behavior of the Green's function and spectral function of an elliptic operator, J. Funct. Anal., 5 (1970), 484-503.
[4] J. Brüning, Zur abschatzung der spektral-function elliptisher operatoren, Math. Z., 137 (1974), 75-85.
[5] S. D. Eidel'man, Parabolic Systems, North-Holland, Amsterdam, 1969.
[6] K. Maruo and H. Tanabe, On the asymptotic distribution of eigenvalues of operators associated with strongly elliptic sesquilinear forms, Osaka J. Math., 8 (1971), 323-345.
[7] K. Maruo, Asymptotic distribution of eigenvalues of non-symmetric operators associated with strongly elliptic sesquilinear forms, Osaka J. Math., 9 (1972), 547-560.
[8] G. Métivier, Estimation du reste en theorie spectrale, in Seminar Analysis 1982/1983, Inst. Math., Berlin (1983), 70-96.
[9] Y. Miyazaki, A sharp asymptotic remainder estimate for the eigenvalues of operators associated with strongly elliptic sesquilinear forms, Japan. J. Math., 15 (1989), 65-97.
[10] Y. Miyazaki, The eigenvalue distribution of elliptic operators with Hölder continuous coefficients, Osaka J. Math., 28 (1991), 935-973.
[11] Y. Miyazaki, The eigenvalue distribution of elliptic operators with Hölder continuous coefficients II, Osaka J. Math., 30 (1993), 267-301.
[12] T. Muramatu, Interpolation Theory and Linear Operators, Iwanami, Tokyo, in Japanese, 1985.
[13] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, New Jersey, 1970.
[14] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North Holland Publ., Amsterdam-New York, 1978.
[15] J. Tsujimoto, On the remainder estimates of asymptotic formula for eigenvalues of operators associated with strongly elliptic sesquilinear forms, J. Math. Soc. Japan, 33 (1981), 557-569.
[16] J. Tsujimoto, On the asymptotic behavior of spectral functions of elliptic operators, Japan. J. Math., 8 (1982), 177-210.
[17] J. Tsujimoto, Asymptotic estimates for spectral functions of elliptic operators and its application, RIMS, Kôkyûroku 530, 17-23, in Japanese, 1984.

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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