Asymptotic expansion of the heat kernel for a class of hypoelliptic operators

Alexander Lopatnikov

Banach Center Publications (1992)

  • Volume: 27, Issue: 2, page 309-316
  • ISSN: 0137-6934

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Lopatnikov, Alexander. "Asymptotic expansion of the heat kernel for a class of hypoelliptic operators." Banach Center Publications 27.2 (1992): 309-316. <http://eudml.org/doc/262733>.

@article{Lopatnikov1992,
author = {Lopatnikov, Alexander},
journal = {Banach Center Publications},
keywords = {asymptotic expansion of the heat kernel},
language = {eng},
number = {2},
pages = {309-316},
title = {Asymptotic expansion of the heat kernel for a class of hypoelliptic operators},
url = {http://eudml.org/doc/262733},
volume = {27},
year = {1992},
}

TY - JOUR
AU - Lopatnikov, Alexander
TI - Asymptotic expansion of the heat kernel for a class of hypoelliptic operators
JO - Banach Center Publications
PY - 1992
VL - 27
IS - 2
SP - 309
EP - 316
LA - eng
KW - asymptotic expansion of the heat kernel
UR - http://eudml.org/doc/262733
ER -

References

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  1. [1] R. Beals and N. Stanton, The heat equation for the ∂̅-Neumann problem I, Comm. Partial Differential Equations 12 (4) (1987), 407-413. Zbl0615.58033
  2. [2] G. Ben Arous, Noyau de la chaleur hypoelliptique et géométrie sous-riemannienne, in: Lecture Notes in Math. 1322, Springer, 1988, 1-16. 
  3. [3] G. Ben Arous, Développement asymptotique du noyau de la chaleur hypoelliptique sur la diagonale, Ann. Inst. Fourier (Grenoble) 39 (1) (1989), 73-99. 
  4. [4] G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat. 13 (1975), 161-207. Zbl0312.35026
  5. [5] B. Helffer et J. Nourrigat, Approximation d'un système de champs de vecteurs et applications à l'hypoellipticité, ibid. 17 (2) (1979), 237-254. Zbl0434.35025
  6. [6] B. Helffer et J. Nourrigat, Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs, Progr. Math. 58, Birkhäuser, 1985. Zbl0568.35003
  7. [7] L. Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147-171. Zbl0156.10701
  8. [8] D. Jerison and A. Sánchez-Calle, Estimates for the heat kernel for a sum of squares of vector fields, Indiana Univ. Math. J. 35 (4) (1986), 835-854. Zbl0639.58026
  9. [9] D. Jerison and A. Sánchez-Calle, Subelliptic second order differential operators, in: Lecture Notes in Math. 1287, Springer, 1988, 46-77. 
  10. [10] A. M. Lopatnikov, Asymptotic behaviour of the spectral function for operators constructed from vector fields, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1987 (3), 76-78 (Moscow Univ. Math. Bull. 42 (3) (1987), 70-72). Zbl0623.47057
  11. [11] A. M. Lopatnikov, Asymptotic behaviour of the spectral function for a class of hypoelliptic operators, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1988 (1), 92-94. 
  12. [12] A. M. Lopatnikov, Spectral asymptotics for a class of hypoelliptic operators, manuscript, Moscow 1987, 94 pp., VINITI no. 2530 B87. 
  13. [13] G. Métivier, Fonction spéctrale et valeurs propres d'une classe d'opérateurs non elliptiques, Comm. Partial Differential Equations 1 (5) (1976), 467-519. Zbl0376.35012
  14. [14] O. Oleĭnik and E. Radkevich, Second Order Equations with Nonnegative Characteristic Form, Amer. Math. Soc., Providence, R.I., 1973. Zbl0217.41502
  15. [15] A. Sánchez-Calle, Fundamental solutions and geometry of the sum of squares of vector fields, Invent. Math. 78 (1984), 143-160. 
  16. [16] L. P. Rothschild, A criterion for hypoellipticity of operators constructed from vector fields, Comm. Partial Differential Equations 4 (1989), 645-699. Zbl0459.35025
  17. [17] L. P. Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent Lie groups, Acta Math. 137 (3-4) (1976), 247-320. Zbl0346.35030
  18. [18] M. Taylor, Noncommutative microlocal analysis, Mem. Amer. Math. Soc. 313 (1984). Zbl0554.35025
  19. [19] T. Taylor, A parametrix for step two hypoelliptic diffusion equations, Trans. Amer. Math. Soc. 296 (1) (1986), 191-215. Zbl0602.35021
  20. [20] N. T. Varopoulos, Analysis on Lie groups, J. Funct. Anal. 76 (1988), 346-410. Zbl0634.22008

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