Prof. Abdelaziz Rhandi on “Ornstein-Uhlenbeck semigroups on star graphs”

In this talk we prove first existence of a classical solution to a
class of parabolic problems with unbounded coefficients on
metric star graphs subject to Kirchhoff-type conditions. The
result is applied to the Ornstein-Uhlenbeck and the harmonic
oscillator operators on metric star graphs. We give an explicit
formula for the associated Ornstein-Uhlenbeck semigroup and
give the unique associated invariant measure. We show that
this semigroup inherit the regularity properties of the classical Ornstein-Uhlenbeck semigroup on R.