Heat Kernels on homogeneous spaces

Journal of the Australian Mathematical Society

C. M. P. A. Smulders¹ 

关键词: primary 43A85;    22D30;    22E25;    22E45;    35K05;   

DOI  :  10.1017/S1446788700015597

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let a1… ad be a basis of the Lie algebra g of a connected Lie group G and let M be a Lie subgroup of,G. If dx is a non-zero positive quasi-invariant regular Borel measure on the homogeneous space X = G/M and S: X × G → C is a continuous cocycle, then under a rather weak condition on dx and S there exists in a natural way a (weakly*) continuous representation U of G in Lp (X;dx) for all p ε [1,].Let Ai be the infinitesimal generator with respect to U and the direction ai, for all i ∈ { 1… d}. We consider n–th order strongly elliptic operators H = ΣcαAα with complex coefficients cα. We show that the semigroup S generated by the closure of H has a reduced heat kernel K and we derive upper bounds for k and all its derivatives.

【 授权许可】

Unknown