On shape preserving semigroups

Details On shape preserving semigroups On shape preserving semigroups

2011-07-25

arxiv.org/abs/1107.5075v2

Mathematics

Functional Analysis

referees comments incorporated. To appear in Archiv der Mathematik (Basel)

Scientific paper

10.1007/s00013-011-0340-4

Motivated by positivity-, monotonicity-, and convexity preserving differential equations, we introduce a definition of shape preserving operator semigroups and analyze their fundamental properties. In particular, we prove that the class of shape preserving semigroups is preserved by perturbations and taking limits. These results are applied to partial delay differential equations.

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