A new L-Antieigenvalue Condition for Ornstein-Uhlenbeck Operators

for simultaneously diagonalizable matrices A,B ∈ C . The unbounded drift term is defined by a skew-symmetric matrix S ∈ R. 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 (R,C ), 1 < p < ∞, is the following L-dissipativity condition |z|2Re 〈w,Aw〉+ (p− 2)Re 〈w, z〉Re 〈z, Aw〉 > γA|z| 2|w|2 ∀ z, w ∈ C