Ornstein–Uhlenbeck semigroups on star graphs
Copyright policy )Ornstein–Uhlenbeck semigroups on star graphs
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 $\mathbb R$.
discrete spectrum, One-parameter semigroups and linear evolution equations, Boundary value problems on graphs and networks for ordinary differential equations, invariant measure, 47D06, 34B45, 35J15, 35K10, FOS: Physical sciences, \(C_0\)-semigroups, Mathematical Physics (math-ph), infinite metric graphs, Mathematics - Spectral Theory, Second-order elliptic equations, harmonic oscillator, Mathematics - Analysis of PDEs, Second-order parabolic equations, Ornstein-Uhlenbeck operators, harmonic oscillator, infinite metric graphs, C0-semigroups, invariant measure, discrete spectrum, FOS: Mathematics, Spectral Theory (math.SP), Mathematical Physics, Ornstein-Uhlenbeck operators, Analysis of PDEs (math.AP)
discrete spectrum, One-parameter semigroups and linear evolution equations, Boundary value problems on graphs and networks for ordinary differential equations, invariant measure, 47D06, 34B45, 35J15, 35K10, FOS: Physical sciences, \(C_0\)-semigroups, Mathematical Physics (math-ph), infinite metric graphs, Mathematics - Spectral Theory, Second-order elliptic equations, harmonic oscillator, Mathematics - Analysis of PDEs, Second-order parabolic equations, Ornstein-Uhlenbeck operators, harmonic oscillator, infinite metric graphs, C0-semigroups, invariant measure, discrete spectrum, FOS: Mathematics, Spectral Theory (math.SP), Mathematical Physics, Ornstein-Uhlenbeck operators, Analysis of PDEs (math.AP)
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