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

MSC:
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. Berlin, Teubner 1935. · JFM 61.0547.01
[2] Friedrichs, K.,Pseudo-differential, operators. New York University, 1968.
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[6] –, Pseudo-differential operators and hypoelliptic equations.Amer. Math. Soc. Symp. Pure Math. 10 (1966),Singular integral operators, 138–183.
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[8] Kuranishi, M., On estimate ||(A(D)+B(x))u(x)||||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 (1966), 473–492. · Zbl 0185.22801 · doi:10.1002/cpa.3160190409
[10] Radkeviĉ, E. V., A priori estimates and hypoelliptic operators with multiple characteristics.Dokl. Akad. Nauk SSSR, 187 (1969), 274–277. Also inSoviet Math. Dokl., 10 (1969), 849–853.
[11] Vaillancourt, R., A simple proof of Lax–Nirenberg theorems.Comm. Pure Appl. Math., 23 (1970), 151–163. · Zbl 0188.41202 · doi:10.1002/cpa.3160230203
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