Download PDF - Analytic hypoellipticity and local solvability for a class of pseudo-differential operators with symplectic characteristicsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Analytic hypoellipticity and local solvability for a class of pseudo-differential operators with symplectic characteristics

Authors 1

Affiliations

  1. Department of Mathematics, Saitama University, 255 Shimo-okubo, Urawa 338, Japan

Bibliography

  1. L. Boutet de Monvel, Hypoelliptic operators with double characteristics and related pseudodifferential operators, Comm. Pure Appl. Math. 27 (1974), 585-639.
  2. L. Boutet de Monvel, A. Grigis et B. Helffer, Paramétrixes d'opérateurs pseudo-différentiels à caractéristiques multiples, Astérisque 34-35 (1976), 93-121.
  3. A. Grigis and L. P. Rothschild, A criterion for analytic hypoellipticity of a class of differential operators with polynomial coefficients, Ann. Math. 118 (1983), 443-460.
  4. V. V. Grushin, On a class of elliptic pseudodifferential operators degenerate on a submanifold, Math. USSR-Sb. 13 (1971), 155-185.
  5. B. Helffer, Sur l'hypoellipticité des opérateurs pseudodifférentiels à caractéristiques multiples (perte de 3/2 dérivées), Bull. Soc. Math. France 51-52 (1977), 13-61.
  6. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1980.
  7. M. Kashiwara, T. Kawai and T. Oshima, Structure of cohomology groups whose coefficients are microfunction solution sheaves of systems of pseudo-differential equations with multiple characteristics I, Proc. Japan Acad. 50 (1974), 420-425.
  8. G. Métivier, Analytic hypoellipticity for operators with multiple characteristics, Comm. Partial Differential Equations, 6 (1981), 1-90.
  9. A. Melin, Parametrix constructions for some right invariant operators on the Heisenberg group, ibid., 1363-1405.
  10. M. Sato, T. Kawai and M. Kashiwara, Microfunctions and Pseudo-Differential Operators, Lecture Notes in Math. 287, Springer, 1973, 265-529.
  11. J. Sjöstrand, Parametrix for pseudodifferential operators with multiple characteristics, Ark. Mat. 12 (1974), 85-130.
  12. E. M. Stein, An example on the Heisenberg group related to the Lewy operator, Invent. Math. 69 (1982), 209-216.
  13. F. Treves, Analytic hypo-ellipticity of a class of pseudodifferential operators with double characteristics and applications, Comm. Partial Differential Equations 3 (1978), 475-642.
  14. F. Treves, Introduction to Pseudodifferential and Fourier Integral Operators, Vols. I, II, Plenum Press, New York and London, 1981.
Banach Center Publications
1996/33/1
Export to PBN, Opens in new tab
Pages:
315-335
Main language of publication
English
Published
1996
Exact and natural sciences