Continuous extension of a densely parameterized semigroup

ar X iv : 0 71 1 . 10 06 v 2 [ m at h . FA ] 1 3 Fe b 20 08 CONTINUOUS EXTENSION OF A DENSELY PARAMETERIZED SEMIGROUP

Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which a...

ar X iv : 0 71 1 . 10 06 v 1 [ m at h . FA ] 7 N ov 2 00 7 CONTINUOUS EXTENSION OF A DENSELY PARAMETERIZED

Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, non-expansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which ...

Parameterized Extension Complexity of Independent Set

Let G be a graph on n vertices and STABk(G) be the convex hull of characteristic vectors of its independent sets of size at most k. It is known that optimizing over STABk(G) is W [1]-hard and is FPT tractable for graphs of bounded expansion. We show analogous results for the extension complexity of STABk(G). In particular, we show that when G is a graph from a class of bounded expansion then xc...

The Critical Spectrum of a Strongly Continuous Semigroup

For a strongly continuous semigroup (T (t))t≥0 with generator A we introduce its critical spectrum σcrit(T (t)). This yields in an optimal way the spectral mapping theorem σ(T (t)) = e ∪ σcrit(T (t)) and improves classical stability results.

A characterization of triple semigroup of ternary functions and Demorgan triple semigroup of ternary functions