# Mitja Nedic: Analytic characterizations of the Lebesgue measure

**Time: **
Wed 2019-12-04 13.15 - 14.14

**Location: **
Kräftriket, house 6, room 306 (Cramér-rummet)

**Participating: **
Mitja Nedic, Stockholms universitet

### Abstract

Each holomorphic function on the poly-upper half-plane with non-negative imaginary part may be uniquely represented by a linear term and a positive Borel measure. Among the measures that appear as representing measures, the Lebesgue measures plays a special role. In this talk, we will present several ways of characterizing the Lebesgue measure among all such measures. Most of these characterizations are analytic in nature, i.e. they are given in terms of integral expressions depending on a continuous parameter. An analogous question for measures on the unit polytorus having vanishing mixed Fourier coefficients will also be discussed.