From resolvent bounds to semigroup bounds
By Bernard Helffer, J. Sjoestrand. 2010
51 citations recorded by the source corpus.
The purpose of this note is to revisit the proof of the Gearhardt-Pr\"uss-Hwang-Greiner theorem for a semigroup S(t), following the general idea of the proofs that we have seen in the literature and to get an explicit estimate on the norm of S(t) in terms of bounds on the resolvent of the generator.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6d6abc3eba56f7647c86ee9a69438d2c7372573d
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In Computational Theory and Mathematics
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In Mathematical Physics
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Citations in the corpus
- Landau Damping: Paraproducts and Gevrey Regularity (2013, methodology): “10,chapterV], which is also used in [38], is to use a Plancherel identity on the resolvent in Hilbert spaces in order to obtain explicit rates of decay on the semigroup in terms of bounds on the resolvent.”
- Factorization for non-symmetric operators and exponential H-theorem (2010, methodology): “Let us also add that this idea was more or less “well-known” in the spectral theory community (as is also acknowledged in [17]), even if it seems hard to”