# Strobl18

Harmonic Analysis and Applications

June 4-8, 2018

Strobl, AUSTRIA

### "The voice transform on the real Blaschke subgroup"

#### Eisner, Tímea

The Blaschke-functions play important role in the theory of analytic functions, in system identification, moreover in the description of congruencies of the hyperbolic geometry of the unit disc. The composition of the Blaschke functions induces a group in the set of the parameters, the so called Blaschke group. In order to construct analytic wavelets Pap and Schipp considered the voice transforms of this group and starting from 2006 published several results connected to this. Instead of the Blascke group , we consider the analogue of it on the interval , the so called real Blaschke group. We introduce a representation of this group. We prove that this representation is unitary, and we consider the voice transform of the real Blaschke group induced by this representation. We use this representation to construct new orthogonal function systems. We construct the characters of the subgroup.

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