1,428 research outputs found
On the spectrum of shear flows and uniform ergodic theorems
The spectra of parallel flows (that is, flows governed by first-order
differential operators parallel to one direction) are investigated, on both
spaces and weighted- spaces. As a consequence, an example of a flow
admitting a purely singular continuous spectrum is provided. For flows
admitting more regular spectra the density of states is analyzed, and spaces on
which it is uniformly bounded are identified. As an application, an ergodic
theorem with uniform convergence is proved.Comment: 18 pages, no figure
Periodic solutions for a class of evolution inclusions
We consider a periodic evolution inclusion defined on an evolution triple of
spaces. The inclusion involves also a subdifferential term. We prove existence
theorems for both the convex and the nonconvex problem, and we also produce
extremal trajectories. Moreover, we show that every solution of the convex
problem can be approximated uniformly by certain extremal trajectories (strong
relaxation). We illustrate our results by examining a nonlinear parabolic
control system
On constructions preserving the asymptotic topology of metric spaces
We prove that graph products constructed over infinite graphs with bounded
clique number preserve finite asymptotic dimension. We also study the extent to
which Dranishnikov's property C, and Dranishnikov and Zarichnyi's straight
finite decomposition complexity are preserved by constructions such as unions,
free products, and group extensions.Comment: 13 pages, accepted for publication in NC Journal of Mathematics and
Statistic
On large indecomposable Banach spaces
Hereditarily indecomposable Banach spaces may have density at most continuum
(Plichko-Yost, Argyros-Tolias). In this paper we show that this cannot be
proved for indecomposable Banach spaces. We provide the first example of an
indecomposable Banach space of density two to continuum. The space exists
consistently, is of the form C(K) and it has few operators in the sense that
any bounded linear operator T on C(K) satisfies T(f)=gf+S(f) for every f in
C(K), where g is in C(K) and S is weakly compact (strictly singular)
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