Variational fractals
Vector-valued holomorphic and harmonic functions
Holomorphic and harmonic functions with values in a Banach space are investigated. Following an approach given in a joint article with Nikolski [4] it is shown that for bounded functions with values in a Banach space it suffices that the composition with functionals in a separating subspace of the dual space be holomorphic to deduce holomorphy. Another result is Vitali’s convergence theorem for holomorphic functions. The main novelty in the article is to prove analogous results for harmonic functions...
Voiculescu’s Entropy and Potential Theory
We give a new proof, relying on polynomial inequalities and some aspects of potential theory, of large deviation results for ensembles of random hermitian matrices.
Volume mean values of subtemperatures
Several authors have found the characteristic mean value formula for temperatures over heat spheres. Those who derived a corresponding formula over heat balls have all chosen different mean values. In this paper we discuss an infinity of possible means over heat balls, and show that, in the wider context of subtemperatures, some are more desirable than others.