Obstructions for uniform stability of C_0-semigroup

Details Obstructions for uniform stability of C_0-semigroup Obstructions for uniform stability of C_0-semigroup

2010-04-12

arxiv.org/abs/1004.1916v1

Siberian Math. J., 2010, v.51, N.2, pp.330-337

Mathematics

Functional Analysis

9 pages

Scientific paper

Let T be a C_0-semigroup on X with generator A. We prove that if the abscissa
of uniform boundedness of the resolvent A is non-negative then for each a
non-decreasing function h:[0,\infty] -> [0,\infty], there are x' in X' and x in
X such that integral from 0 to \infty of h(|< x',T(t)x)>| is equal to \infty.
If Sp(A) contained a number from iR then such x may be taken in D(A^\infty).

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