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2 votes
0 answers
175 views

Eigenvalues of Laplace operator and Schrödinger operator

When reading the paper Control for Schrödinger operators on tori by N.Burq and M.Zworski (Math. Res. Lett., 19(2):309–324, 2012), an inequality confused me: Define the flat torus $\mathbb{T}^2=\mathbb{...
1 vote
0 answers
92 views

Semigroup theory for non-symmetric Markov processes / complex-valued potentials

Let $X$ be a continuous-time Markov process on a countable state space $E$, and let $V:E\mapsto\mathbb C$ be some complex function. $X$ can be characterized by its transition rates $(\lambda_{xy})_{x,...