On the remainder estimates of asymptotic formulas for eigenvalues of operators associated with strongly elliptic sesquilinear forms

Jun-ichi TSUJIMOTO

doi:10.2969/jmsj/03340557

Jun-ichi TSUJIMOTO

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1981 Volume 33 Issue 4 Pages 557-569

DOI https://doi.org/10.2969/jmsj/03340557

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Published: 1981 Received: November 29, 1979 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Right : [1] S. Agmon, Lectures on Elliptic Boundary Value Problems, Van Nostrand Mathematical Studies, Princeton, 1965.
[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. Functional Analysis, 5 (1970), 484-503.
[4] 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.
[5] K. Maruo, Asymptotic distribution of eigenvalues of non-symmetric operators associated with strongly elliptic sesquilinear forms, Osaka J. Math., 9 (1972), 547-560.
[6] G. Metivier, Valeurs propres des problemes aux limites elliptiques irreguliers, Bull. Soc. Math. France Mem., 51-52 (1977), 125-219.
[7] D. Robert, Sur la repartition du spectre d'operateurs elliptiques non auto-adjoints a coefficients irreguliers, Osaka J. Math., 14 (1977), 593-607.
[8] R. T. Seeley, A sharp asymptotic remainder estimate for the eigenvalues of the Laplacian in a domain of R³, Advances in Math., 29 (1978), 244-269.
[9] H. Tanabe, On Green's functions of elliptic and parabolic boundary values problems, Proc. Japan Acad., 48 (1972), 709-711.
[10] H. Tanabe, On remainder estimates in the asymptotic formula of elliptic operators, Proc. Japan Acad., 48 (1972), 377-380.
[11] J. Tsujimoto, On the asymptotic behavior of spectral functions of elliptic operators, to appear.

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