Hypoelliptic heat kernel inequalities on Lie groups
نویسندگان
چکیده
منابع مشابه
The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups
We present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp’s volume form introduced by Montgomery. This definition generalizes the one of the Laplace-Beltrami operator in Riemannian geometry. In the case of left-invariant problems on unimodular Lie groups we prove that it coincides with the usual sum of squares. We t...
متن کاملInformation-Theoretic Inequalities on Unimodular Lie Groups
Classical inequalities used in information theory such as those of de Bruijn, Fisher, Cramér, Rao, and Kullback carry over in a natural way from Euclidean space to unimodular Lie groups. These are groups that possess an integration measure that is simultaneously invariant under left and right shifts. All commutative groups are unimodular. And even in noncommutative cases unimodular Lie groups s...
متن کاملHeat Kernel Analysis on Infinite-dimensional Groups
The paper gives an overview of our previous results concerning heat kernel measures in infinite dimensions. We give a history of the subject first, and then describe the construction of heat kernel measure for a class of infinite-dimensional groups. The main tool we use is the theory of stochastic differential equations in infinite dimensions. We provide examples of groups to which our results ...
متن کاملHeinz-Kato’s inequalities for semisimple Lie groups
Extensions of Heinz-Kato’s inequalities and related inequalities are obtained for semisimple connected noncompact Lie groups. Mathematics Subject Index 2000: Primary 22E46; Secondary 15A45
متن کاملSEMINAR ON LIE GROUPS 1. Lie Groups
Example 1.3. (R,+) Example 1.4. S or T n = S × ...× S Example 1.5. Gl (n,F) ⊆ F, where F = R or C Example 1.6. E3 = isometries of R (2 connected components) Let the orthogonal group O3 < E3 be the subgroup that fixes the origin, and let the special orthogonal group SO (3) = SO3 < O3 be the orientation-preserving elements of O3. Visualizing SO (3): Let u be a vector of length l in R, correspondi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2008
ISSN: 0304-4149
DOI: 10.1016/j.spa.2007.04.012