A new L^p-Antieigenvalue Condition for Ornstein-Uhlenbeck Operators

2015/10/03 by Denny Otten, Otten, Denny
Computer Science · Mathematics · #35A02 #35J47 (47B44 #47A10) #47D06 #Analysis of PDEs (math.AP) #FOS: Mathematics #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1510.00864

openalex publication_date 2015/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study perturbed Ornstein-Uhlenbeck operators [ L_∞ v](x) = A\triangle v(x) + ⟨ Sx,∇ v(x)⟩-B v(x), x∈ℝ^d, d\geqslant 2, for simultaneously diagonalizable matrices A,B∈ℂ^N,N. The unbounded drift term is defined by a skew-symmetric matrix S∈ℝ^d,d. Differential operators of this form appear when investigating rotating waves in time-dependent reaction diffusion systems. As shown in a companion paper, one key assumption to prove resolvent estimates of L_∞ in L^p(ℝ^d,ℂ^N), 10. We prove that the L^p-dissipativity condition is equivalent to a new L^p-antieigenvalue condition \beginalign* A invertible and μ₁(A) > (|p-2|)/(p), 1

Citations

• On the Theory of the Brownian Motion

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