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Geometric and Potential Theoretic Results on Lie Groups

  • N. Th. Varopoulos (a1)
Abstract

The main new results in this paper are contained in the geometric Theorems 1 and 2 of Section 0.1 below and they are related to previous results of M. Gromov and of myself (cf. [11], [29]). These results are used to prove some general potential theoretic estimates on Lie groups (cf. Section 0.3) that are related to my previous work in the area (cf. [28], [34]) and to some deep recent work of G. Alexopoulos (cf. [3], [4]).

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References
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[25] Varopoulos, N. Th., Information theory and harmonic functions. Bull. Sci. Math. 110(1986), 347389.
[26] Varopoulos, N. Th., Convolution powers on locally compact groups. Bull. Sci. Math 111(1987), 333342.
[27] Varopoulos, N. Th., Analysis on Lie groups. Rev. Mat. Iberoamericana (3) 12(1996), 791917.
[28] Varopoulos, N. Th., The local theorem for symmetric diffusion on Lie groups, an overview. CMS Conf. Proc. 21(1997), 143152.
[29] Varopoulos, N. Th., Distance distortion on Lie groups. Institute Mittag-Leffler Report 31, 1995/96, and Random walks discrete potential theory Proceedings Costona (1997), Symposia Mathematica 39(1999) (eds. Picardello, M. A and Woess, W.), Cambridge University Press.
[30] Varopoulos, N. Th., A geometric classification of Lie groups. Rev. Mat. Iberoamericana, to appear 2000.
[31] Varopoulos, N. Th., Analysis on Lie groups, II. To appear.
[32] Varopoulos, N. Th., Saloff-Coste, L. and Coulhon, T., Analysis and geometry on groups. Cambridge Tracts in Mathematics 100, Cambridge University Press, 1992.
[33] Varopoulos, N. Th., Wiener-Hopf theory and nonunimodular groups. J. Funct. Anal. (2) 120(1994), 467483.
[34] Varopoulos, N. Th., Diffusion on Lie groups I, II, III. Canad. J. Math. 46(1994), 438448. 1073–1992; 48(1996), 641–672.
[35] Varopoulos, N. Th. and S. Mustapha, forthcoming book. Cambridge University Press.
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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