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arXiv · 2109.12369

Ornstein--Uhlenbeck Semigroups on Star Graphs

Delio Mugnolo·Abdelaziz Rhandi
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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 $\mathbb R$.

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Delio Mugnolo, Abdelaziz Rhandi. 2021-09-25. Ornstein--Uhlenbeck Semigroups on Star Graphs. https://arxiv.org/abs/2109.12369

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