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1992 | 27 | 2 | 309-316
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
27
Numer
2
Strony
309-316
Opis fizyczny
Daty
wydano
1992
Twórcy
  • Space Research Institute, Russian Academy of Sciences, Profsoyuznaya 84/32, Moscow, 117810 Russia
Bibliografia
  • [1] R. Beals and N. Stanton, The heat equation for the ∂̅-Neumann problem I, Comm. Partial Differential Equations 12 (4) (1987), 407-413.
  • [2] G. Ben Arous, Noyau de la chaleur hypoelliptique et géométrie sous-riemannienne, in: Lecture Notes in Math. 1322, Springer, 1988, 1-16.
  • [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] G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat. 13 (1975), 161-207.
  • [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.
  • [6] B. Helffer et J. Nourrigat, Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs, Progr. Math. 58, Birkhäuser, 1985.
  • [7] L. Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147-171.
  • [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.
  • [9] D. Jerison and A. Sánchez-Calle, Subelliptic second order differential operators, in: Lecture Notes in Math. 1287, Springer, 1988, 46-77.
  • [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).
  • [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] A. M. Lopatnikov, Spectral asymptotics for a class of hypoelliptic operators, manuscript, Moscow 1987, 94 pp., VINITI no. 2530 B87.
  • [13] G. Métivier, Fonction spéctrale et valeurs propres d'une classe d'opérateurs non elliptiques, Comm. Partial Differential Equations 1 (5) (1976), 467-519.
  • [14] O. Oleĭnik and E. Radkevich, Second Order Equations with Nonnegative Characteristic Form, Amer. Math. Soc., Providence, R.I., 1973.
  • [15] A. Sánchez-Calle, Fundamental solutions and geometry of the sum of squares of vector fields, Invent. Math. 78 (1984), 143-160.
  • [16] L. P. Rothschild, A criterion for hypoellipticity of operators constructed from vector fields, Comm. Partial Differential Equations 4 (1989), 645-699.
  • [17] L. P. Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent Lie groups, Acta Math. 137 (3-4) (1976), 247-320.
  • [18] M. Taylor, Noncommutative microlocal analysis, Mem. Amer. Math. Soc. 313 (1984).
  • [19] T. Taylor, A parametrix for step two hypoelliptic diffusion equations, Trans. Amer. Math. Soc. 296 (1) (1986), 191-215.
  • [20] N. T. Varopoulos, Analysis on Lie groups, J. Funct. Anal. 76 (1988), 346-410.
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Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv27z2p309bwm
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