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 inherits the regularity properties of the classical Ornstein-Uhlenbeck semigroup on R.
ORNSTEIN-UHLENBECK SEMIGROUPS ON STAR GRAPHS
Rhandi Abdelaziz
2022-01-01
Abstract
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 inherits the regularity properties of the classical Ornstein-Uhlenbeck semigroup on R.File in questo prodotto:
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