Convex conjugates of analytic functions of logarithmically convex functionals

Krzysztof Zajkowski

Let $f_{\mathbf{c}}(r)={\sum }_{n=0}^{\infty }{e}^{c_n}{r}^n$ be an analytic function; $\mathbf{c}=(c_n)\in l_{\infty }$. We assume that $r$ is some logarithmically convex and lower semicontinuous fun…