Explore >> Select a destination
|
You are here 
|
stevensoojin.kim | ||
| | | | |
djalil.chafai.net
|
|
| | | | | This post is mainly devoted to a probabilistic proof of a famous theorem due to Schoenberg on radial positive definite functions. Let us begin with a general notion: we say that \( {K:\mathbb{R}^d\times\mathbb{R}^d\rightarrow\mathbb{R}} \) is a positive definite kernel when \[ \forall n\geq1, \forall x_1,\ldots,x_n\in\mathbb{R}^d, \forall c\in\mathbb{C}^n, \quad\sum_{i=1}^n\sum_{j=1}^nc_iK(x_i,x_j)\bar{c}_j\geq0. \] When \( {K} \) is symmetric, i.e. \( {K(x,y)=K(y,x)} \) for... | |
| | | | |
fabricebaudoin.blog
|
|
| | | | | In this lecture, we studySobolev inequalities on Dirichlet spaces. The approach we develop is related to Hardy-Littlewood-Sobolev theory The link between the Hardy-Littlewood-Sobolev theory and heat kernel upper bounds is due to Varopoulos, but the proof I give below I learnt it from my colleague RodrigoBañuelos. It bypasses the Marcinkiewicz interpolation theorem,that was originally used... | |
| | | | |
francisbach.com
|
|
| | | | | ||
| | | | |
thenumb.at
|
|
| | | |||
