Large time estimates for non-symmetric heat kernel on the affine group

Camillo Melzi

Annales mathématiques Blaise Pascal (2002)

  • Volume: 9, Issue: 1, page 63-78
  • ISSN: 1259-1734

How to cite

top

Melzi, Camillo. "Large time estimates for non-symmetric heat kernel on the affine group." Annales mathématiques Blaise Pascal 9.1 (2002): 63-78. <http://eudml.org/doc/79243>.

@article{Melzi2002,
author = {Melzi, Camillo},
journal = {Annales mathématiques Blaise Pascal},
keywords = {affine group; Laplacian with drift; heat kernel; large time upper estimate},
language = {eng},
number = {1},
pages = {63-78},
publisher = {Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal},
title = {Large time estimates for non-symmetric heat kernel on the affine group},
url = {http://eudml.org/doc/79243},
volume = {9},
year = {2002},
}

TY - JOUR
AU - Melzi, Camillo
TI - Large time estimates for non-symmetric heat kernel on the affine group
JO - Annales mathématiques Blaise Pascal
PY - 2002
PB - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
VL - 9
IS - 1
SP - 63
EP - 78
LA - eng
KW - affine group; Laplacian with drift; heat kernel; large time upper estimate
UR - http://eudml.org/doc/79243
ER -

References

top
  1. [1] G. Alexopoulos. Sublaplacians on groups of polynomial growth. Mem. Amer. Math. Soc., to appear. Zbl0908.22013MR1878341
  2. [2] R. Azencott. Géodésiques et diffusions en temps petit. Astérisque, 84-85:17-31, 1981. Zbl0507.60070MR634964
  3. [3] Ph. Bougerol. Comportement asymptotique des puissances de convolution d'une probabilité sur un espace symétrique. Astérisque, 74:29-45, 1980. Zbl0463.60009MR588156
  4. [4] E.B. Davies and N. Mandouvalos. Heat bounds on hyperbolic space and Kleinian groups. Proc. London Math. Soc. (3), 52:182-208, 1988. Zbl0643.30035MR940434
  5. [5] A. Grigor'yan. Gaussian upper bounds for the heat kernel on arbitrary manifolds. J. Differential Geometry, 45:33-52, 1997. Zbl0865.58042MR1443330
  6. [6] A. Grigor'yan. Estimates of heat kernels on Riemannian manifolds. In B. Davies and Yu. Safarov, editors, Spectral Theory and Gemetry. Edinburgh 1998, pages 140-225. London Math. Soc. Lectures Nte Series 273, Cambridge Univ. Press, 1998. Zbl0985.58007MR1736868
  7. [7] G.A. Hunt. Semi-groups of measures on Lie groups. A.M.S., 81:264-293, 1956. Zbl0073.12402MR79232
  8. [8] S. Mustapha. Gaussian estimates for heat kernels on Lie groups. Math. Proc. Camb. Phil. Soc., 128:45-64, 2000. Zbl0947.22007MR1724427
  9. [9] A. Nagel, E. Stein, and M. Wainger. Balls and metrics defined by vector fields. Acta Math., 155:103-147, 1985. Zbl0578.32044MR793239
  10. [10] V.I. Ushakov. Stabilization of solutions of the third mixed problem for a second order parabolic equation in a non-cyclic domain (Engl. trans.). Math. USSR Sb., 39:87-105, 1981. Zbl0462.35048MR560465
  11. [11] N. Varopoulos. Small time gaussian estimates of heat diffusion kernels. Part I: The semi-group technique. Bull. Sc. Math., 113:253-277, 1989. Zbl0703.58052MR1016211
  12. [12] N. Varopoulos. Small time gaussian estimates of heat diffusion kernels. Part II: The theory of large deviations. J. Funct. Anal., 93:1-33, 1990. Zbl0712.58056MR1070036
  13. [13] N. Varopoulos. Analysis on Lie groups. Rev. Mat. Iberoamericana, 12:791-917, 1996. Zbl0881.22009MR1435484
  14. [14] N. Varopoulos and S. Mustapha. Forthcoming book. Cambridge University Press. 
  15. [15] N. Varopoulos, L. Saloff-Coste, and Th. Coulhon. Analysis and geometry on groups. Cambridge Univ. Press, Cambridge, 1992. Zbl1179.22009MR1218884

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.