On the eigenvalues of a class of hypoelliptic operators. (English) Zbl 0375.35014


35H10 Hypoelliptic equations
35P20 Asymptotic distributions of eigenvalues in context of PDEs
Full Text: DOI EuDML


[1] Bolley, C., Camus, J., Pham, T.: Colloque d’?quations aux d?riv?es partielles de St-Jean-de-Monts (June 1977). Lecture Notes in Mathematics. Berlin, Heidelberg, New York: Springer (to appear)
[2] Boutet de Monvel, L.: Hypoelliptic operators with double characteristics and related pseudo-differential operators. Comm. Pure Appl. Math.27, 585-639 (1974) · Zbl 0294.35020 · doi:10.1002/cpa.3160270502
[3] Boutel de Monvel, L., Treves, F.: On a dass of pseudo-differential operators with double characteristics. Invent. Math.24, 1-34 (1974) · Zbl 0281.35083 · doi:10.1007/BF01418785
[4] Boutel de Monvel, L., Treves, F.: On a class of pseudo-differential equations with double characteristics. Comm. Pure Appl. Math.27, 59-89 (1974) · Zbl 0286.35065 · doi:10.1002/cpa.3160270105
[5] Gaveau, B.: Principe de moindre action, propagation de la chaleur et estim?es sous elliptiques sur certains groupes nilpotents. Acta Math.139 (1977) · Zbl 0366.22010
[6] H?rmander, L.: The spectral function of an elliptic operator. Acta Math.121, 193-218 (1968) · Zbl 0164.13201 · doi:10.1007/BF02391913
[7] Karamata, J.: Neuer Beweis und Verallgemeinerung der Tauberschen S?tze welche die Laplacesche und Stieltijesche Transformationen betreffen. J. Reine u. Angew. Math.164, 27-39 (1931) · JFM 57.0262.01 · doi:10.1515/crll.1931.164.27
[8] Kucherenko, V.: Asymptotic solutions of equations with complex characteristics. Math. Sb.137, 163-213 (1974) · Zbl 0311.35007
[9] Melin, A.: Lower bounds for pseudo-differential operators. Arkiv f?r Math.9, 117-140 (1971) · Zbl 0211.17102 · doi:10.1007/BF02383640
[10] Melin, A., Sj?strand, J.: Fourier integral operators with complex-valued phase functions. Lecture Notes in Mathematics 459, pp. 120-233. Berlin, Heidelberg, New York: Springer 1975 · Zbl 0306.42007
[11] Melin, A., Sj?strand, J.: Fourier integral operators with complex phase functions and a parametrix for an interior boundary value problem. Comm. P.D.E.1, 313-400 (1976) · Zbl 0364.35049 · doi:10.1080/03605307608820014
[12] Metivier, G.: Fonction spectrale et valeurs propres d’une class d’operateurs non elliptiques. Comm. P.D.E.1, 467-519 (1976) · Zbl 0376.35012 · doi:10.1080/03605307608820018
[13] Sj?strand, J.: Parametrices for pseudodifferential operators with multiple characteristics. Arkiv f?r Mat.12, 85-130 (1974) · Zbl 0317.35076 · doi:10.1007/BF02384749
[14] Sj?strand, J.: Applications of Fourier distributions with complex phase function. Lecture Notes in Mathematics 459, 255-282. Berlin, Heidelberg, New York: Springer 1975
[15] Treves, F.: Solution of Cauchy problems modulo flat functions. Comm. P.D.E.1, 45-72 (1976) · doi:10.1080/03605307608820003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.