Homogenization and Kernel Bounds
Nick Dungey, A. F. M. ter Elst, Derek W. Robinson · Birkhäuser Boston eBooks · 2003
In this chapter we return to the analysis of complex subelliptic operators H , as defined in Section II.2, and the associated semigroup kernels K on groups G of polynomial growth. The eventual aim is to understand the global properties of the kernels and the global geometry of the group. The starting point is the observation that if G is simply connected, then G is the semidirect product M × Q of a compact Levi subgroup M and the group radical Q . Moreover, it follows from the analysis of Section III.7 that G = ( M × Q N , S *) where Q N is the nilshadow of Q and the group product S * is defined with the homomorphism S given by (III.44). Therefore the theory can be reformulated on the simpler direct product group G N = M × Q N , the shadow of G . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.