# On a theorem of Grigorʹyan, Hu and Lau

by Luke Rogers

We refine a result of Grigorʹyan, Hu and Lau to give a moment condition on a heat kernel which characterizes the critical exponent at which a family of Besov spaces associated to the Dirichlet energy becomes trivial. Continue reading

# Detecting stable scales in images via non-smooth K-functionals

by Triet M. Le and Luke Rogers

In image decompositions, one is interested in decomposing $$f$$ into $$u+v$$ where $$u$$ and $$v$$ have different features. In a variational approach, such a decomposition is achieved by solving the following variational problem
$$\inf_{(u,v)∈X1×X2} \{ tF_1(u) + F_2(v) : f = u + v\}$$, Continue reading