Article PDF
Avoid common mistakes on your manuscript.
References
R. Beals,Propagation of singularities for D1/2- □band similar operators (preprint).
L. Boutet de Monvel,Hypoelliptic equations with double characteristics and related pseudodifferential operators, Commun. Pure Appl. Math.27 (1974), 585–639.
L. Boutet de Monvel, A. Grigis and B. Helffer,Parametrixes d’opérateurs pseudo-differentials à caracteristique multiple, Asterisque34-35 (1976).
J. Chazarain,Formule de Poisson pour les variétés remanniennes, Invent. Math.24 (1974), 65–82.
J. J. Duistermaat and V. W. Guillemin,The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math.29 (1975), 39–79.
I. M. Gel’fand and G. E. Shilov,Generalized Functions, Academic Press, New York, 1967.
V. W. Guillemin and S. Sternberg,The metaplectic representation, Weyl operators and spectral theory, J. Funct. Anal.42 (1981), 128–225.
L. Hörmander,Pseudo-differential operators, Commun. Pure Appl. Math.18 (1965), 501–527.
L. Hörmander,The spectral function of an elliptic operator, Acta Math.121 (1968), 193–218.
L. Hörmander,Fourier integral operators, I, Acta Math.127 (1971), 89–183.
L. Hörmander,A class of hypoelliptic operators with double characteristics, Math. Ann.217 (1975), 165–188.
L. Hörmander.The Cauchy problem for differential equations with double characteristics, J. Analyse Math.32 (1977), 110–196.
V. Y. Ivriiand V. M. Petkov,Necessary conditions for the correctness of the Cauchy problem for non-strictly hyperbolic equations, Russian Math. Surveys5 (1974), (1974), 1–70.
R. Lascar, Thèse de doctorat d’Etat Paris-7, 1979.
B. Lascar,Propagation des singularités pour des équations hyperboliques à caracteristiques de multiplicité au plus double et singularités Masloviennes, Am. J. Math.104 (1982), 227–285.
B. Lascar and R. Lacar,Propagation des singularités pour des équations hyperboliques à caracteristiques de multiplicité au plus double et singularités Masloviennes, J. Analyse Math.41 (1982), 1–38.
A. Melin,Lower bounds for pseudo-differentials. Ark. Mat.9 (1971), 117–140.
R. B. Melrose and G. A. Uhlmann,Lagrangian intersection and the Cauchy problem, Commun. Pure Appl. Math.32 (1979), 483–519.
R. B. Melrose,Hypoelliptic operators with characteristic variety of codimension two and the wave equation, Séminaire Goulaouic-Schwartz 1979–1980, exposé 11.
R. B. Melrose,Equivalence of glancing hypersurfaces II, Math. Ann.255 (1981), 159–198.
A. Menikoff,Hypoelliptic operators with double characteristics, inSeminar on Singularities of Solutions of Linear Partial Differential Equations, L. Hörmander, ed., Princeton University Press, 1979.
A. Menikoff and J. Sjöstrand,On the eigenvalues of a class of hypoelliptic operators, Math. Ann.235 (1978), 55–85.
R. T. Seeley,Complex powers of an elliptic operator, Proc. Symp. Pure Math.10 (1968), 288–307.
A Weinstein,Lectures on Symplectic Manifolds, CBMS No. 29, Am. Math. Soc., 1977.
Author information
Authors and Affiliations
Additional information
This work was supported in part by the National Science Foundation under grant MCS-8006521.
Rights and permissions
About this article
Cite this article
Melrose, R.B. The wave equation for a hypoelliptic operator with symplectic characteristics of codimension two. J. Anal. Math. 44, 134–182 (1984). https://doi.org/10.1007/BF02790194
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02790194