zbMATH — the first resource for mathematics

A class of hypoelliptic pseudodifferential operators with double characteristics. (English) Zbl 0306.35032

35H10 Hypoelliptic equations
35S05 Pseudodifferential operators as generalizations of partial differential operators
Full Text: DOI EuDML
[1] 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
[2] Boutet de Monvel, L., Trèves, F.: On a class of pseudo-differential operators with double characteristics. Inventiones math.24, 1-34 (1974) · Zbl 0281.35083 · doi:10.1007/BF01418785
[3] Calderón, A. P., Vaillancourt, R.: A class of bounded pseudo-differential operators. Proc. Nat. Acad. Sci. USA69, 1185-1187 (1972) · Zbl 0244.35074 · doi:10.1073/pnas.69.5.1185
[4] Grigis, A.: Hypoellipticité pour une class d’opérateurs pseudodifférentiels à caractéristiques doubles et paramétrix associés. C. R. Acad. Sci. Paris (to appear)
[5] Gru?in, V. V.: On a class of hypoelliptic operators. Mat. Sbornik83, 456-473 (1970). Also in Math. USSR Sbornik12, 458-476 (1970)
[6] Gru?in, V. V.: Pseudodifferential operators in ? n with bounded symbols. Funkt. anal. i evo pril.43, 37-50 (1970). Also in Funct. Anal. Appl.4, 202-212 (1970)
[7] Hörmander, L.: Pseudo-differential operators and non-elliptic boundary problems. Ann. of Math.83, 129-209 (1966) · Zbl 0132.07402 · doi:10.2307/1970473
[8] Hörmander, L.: Pseudo-differential operators and hypoelliptic equations. A.M.S. Proc. Symp. Pure Math.10, 138-183 (1967) · Zbl 0167.09603
[9] Ivrii, V. Ia., Petkov, V. M.: Necessary conditions for the correctness of the Cauchy problem for non-strictly hyperbolic equations. Usp. Mat. Nauk29, 3-70 (1974) · Zbl 0312.35049
[10] Melin, A.: Lower bounds for pseudo-differential operators. Ark. för Mat.9, 117-140 (1971) · Zbl 0211.17102 · doi:10.1007/BF02383640
[11] Radkevi?, E. V.: A priori estimates and hypoelliptic equations with multiple characteristics. Dokl. Akad. Nauk SSSR187, 274-277 (1969). Also in Soviet Math. Doklady10, 849-853 (1969)
[12] Segal, I. E.: Transforms for operators and symplectic automorphics over a locally compact abelian group. Math. Scand.13, 31-43 (1963) · Zbl 0208.39002
[13] Sjöstrand, J.: Parametrices for pseudodifferential operators with multiple characteristics. Ark. för Mat.12, 85-130 (1974) · Zbl 0317.35076 · doi:10.1007/BF02384749
[14] Weil, A.: Sur certains groupes d’opérateurs unitai res. Acta Math.111, 143-211 (1964) · Zbl 0203.03305 · doi:10.1007/BF02391012
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.