Asymptotics for the heat kernel on H-type groups
نویسندگان
چکیده
منابع مشابه
The Heat Kernel for H-type Groups
Theorem 1 gives an explicit formula for the heat kernel on an H -type group. Folland (2] has shown that for stratified nilpotent Lie groups the heat semigroup is a semigroup of kernel operators on LP, 1 5 p < oo and on Co. Cygan (1] has obtained formulas for heat kernels for any two step nilpotent simply connected Lie group. Cygan found the heat kernel for a free simply connected two step nilpo...
متن کاملGradient Estimates for the Subelliptic Heat Kernel on H-type Groups
We prove the following gradient inequality for the subelliptic heat kernel on nilpotent Lie groups G of H-type: |∇Ptf | ≤ KPt(|∇f |) where Pt is the heat semigroup corresponding to the sublaplacian on G, ∇ is the subelliptic gradient, and K is a constant. This extends a result of H.-Q. Li [10] for the Heisenberg group. The proof is based on pointwise heat kernel estimates, and follows an approa...
متن کاملPrecise Estimates for the Subelliptic Heat Kernel on H-type Groups
We establish precise upper and lower bounds for the subelliptic heat kernel on nilpotent Lie groups G of H-type. Specifically, we show that there exist positive constants C1, C2 and a polynomial correction function Qt on G such that C1Qte − d2 4t ≤ pt ≤ C2Qte d2 4t where pt is the heat kernel, and d the Carnot-Carathéodory distance on G. We also obtain similar bounds on the norm of its subellip...
متن کاملStochastic Taylor expansions and heat kernel asymptotics
3 Stochastic Taylor expansions 5 3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Chen series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 Brownian Chen series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Exponential of a vector field . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.5 Li...
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 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: Annali di Matematica Pura ed Applicata (1923 -)
سال: 2017
ISSN: 0373-3114,1618-1891
DOI: 10.1007/s10231-017-0713-9