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On Green’s functions of elliptic and parabolic boundary value problems. (English) Zbl 0277.35042

MSC:
35J30 Higher-order elliptic equations
35J40 Boundary value problems for higher-order elliptic equations
35B45 A priori estimates in context of PDEs
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
35P05 General topics in linear spectral theory for PDEs
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[1] S. Agmon: On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems. Comm. Pure Appl. Math., 15, 119-147 (1962). · Zbl 0109.32701 · doi:10.1002/cpa.3160150203
[2] S. Agmon: On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems. Comm. Pure Appl. Math., 18, 627-663 (1965). · Zbl 0151.20203 · doi:10.1002/cpa.3160180405
[3] R. Arima: On general boundary value problems for parabolic equations. J. Math. Kyoto Univ., 4, 207-243 (1964). · Zbl 0143.13902
[4] R. Beals: Asymptotic behavior of the Green’s function and spectral function of an elliptic operator. J. Func. Anal., 5, 484-503 (1970). · Zbl 0195.11401 · doi:10.1016/0022-1236(70)90021-2
[5] F. E. Browder: On the spectral theory of elliptic differential operators. I. Math. Ann., 142, 22-130 (1961). · Zbl 0104.07502 · doi:10.1007/BF01343363 · eudml:160823
[6] F. E. Browder: A continuity property for adjoints of closed operators in Banach spaces, and its application to elliptic boundary value problems. Duke Math. J., 28, 157-182 (1961). · Zbl 0102.31502 · doi:10.1215/S0012-7094-61-02815-0
[7] L. Hormander: On the Riesz Means of Spectral Functions and Eigen-function Expansions for Elliptic Differential Operators. Lecture at the Belfer Graduate School. Yeshiva University (1966).
[8] K. Masuda: Manuscript for Seminar at Kyoto University (1970).
[9] H. B. Stewart: Generation of analytic semigroups by strongly elliptic operators (to appear). · Zbl 0264.35043 · doi:10.2307/1996879
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