Difference estimates for continuous and discrete operator semigroups |
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Authors: | Nick Dungey |
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Institution: | (1) Department of Mathematics, Macquarie University, Sydney, NSW, 2109, Australia |
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Abstract: | For suitable bounded operator semigroups (e
tA
)
t≥0 in a Banach space, we characterize the estimate ‖Ae
tA
‖≤c/F(t) for large t, where F is a function satisfying a sublinear growth condition. The characterizations are by holomorphy estimates on the semigroup,
and by estimates on powers of the resolvent. We give similar characterizations of the difference estimate ‖T
n
−T
n+1‖≤c/F(n) for a power-bounded linear operator T, when F(n) grows faster than n
1/2 for large n. |
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Keywords: | C 0-semigroup Analytic semigroup Power-bounded operator Resolvent estimate |
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