Lower bounds for pseudo-differential operators. (English) Zbl 0211.17102


47G30 Pseudodifferential operators
47A75 Eigenvalue problems for linear operators
35S05 Pseudodifferential operators as generalizations of partial differential operators
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[1] Carathéodory, C., Variationsrechnung und partielle Differentialgleichungen erster Ordnung (1935), Berlin: Teubner, Berlin · JFM 61.0547.01
[2] Friedrichs, K.,Pseudo-differential, operators. New York University, 1968.
[3] Gårding, L., Dirichlet’s problem for linear elliptic partial differential equations, Math. Scand., 1, 55-72 (1953) · Zbl 0053.39101
[4] Hörmander, L., Fourier Integral Operators I, Acta Math., 127, 79-183 (1971) · Zbl 0212.46601
[5] Hörmander, L., Pseudo-differential operators and non-elliptic boundary problems, Ann. of Math., 83, 129-209 (1966) · Zbl 0132.07402
[6] Hörmander, L., Pseudo-differential operators and hypoelliptic equations, Amer. Math. Soc. Symp. Pure Math., 10, 138-183 (1966)
[7] Kohn, J. J.; Nirenberg, L., An algebra of pseudo-differential operators, Comm. Pure Appl. Math., 18, 269-305 (1965) · Zbl 0171.35101
[8] Kuranishi, M., On estimate ‖(A(D)+B(x))u(x)‖≧c‖u‖.Amer. Math. Soc. Lecture notes, Summer Institute, Global analysis, 1968.
[9] Lax, P. D.; Nirenberg, L., On stability for difference schemes; a sharp form of Gårding’s inequality, Comm. Pure Appl. Math., 19, 473-492 (1966) · Zbl 0185.22801
[10] Radkeviĉ, E. V., A priori estimates and hypoelliptic operators with multiple characteristics, Dokl. Akad. Nauk SSSR, 187, 274-277 (1969)
[11] Vaillancourt, R., A simple proof of Lax—Nirenberg theorems, Comm. Pure Appl. Math., 23, 151-163 (1970) · Zbl 0188.41202
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