Semigroup Growth Bounds

E B Davies

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arXiv · math/0302144

Semigroup Growth Bounds

E B Davies

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Abstract

We prove lower bounds on $||T_t||$, where $T_t$ 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 Schrödinger operator, but the semigroup growth is measured using the $L^1$ norm rather than the $L^2$ norm. Numerical confirmation of the results is provided.

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BibTeX RIS

E B Davies. 2003-02-12. Semigroup Growth Bounds. https://arxiv.org/abs/math/0302144

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