# 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

# Estimates for the resolvent kernel of the Laplacian on p.c.f. self similar fractals and blowups

by Luke G. Rogers

We provide a method for obtaining upper estimates of the resolvent kernel of the Laplacian on a post-critically finite self-similar fractal that relies on a self-similar series decomposition of the resolvent. Continue reading