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Spectrum, resolvent, numerical range, functional calculus, operator semigroups. Special classes of operators: compact, Fredholm, dissipative, differential, integral, pseudodifferential, etc.

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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 …
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