Semigroup Growth Bounds
Abstract
We prove lower bounds on ||Tt||, where Tt is a one-parameter semigroup, starting from information on the resolvent norms, i.e. the pseudospectra. We provide a physically important example in which the growth of the semigroup norm cannot be derived from spectral information. The generator is a self-adjoint Schr\"odinger operator, but the semigroup growth is measured using the L1 norm rather than the L2 norm. Numerical confirmation of the results is provided.
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