A note on self-extremal sets in Lp(Ω) spaces

L p CHRISTOFFEL FUNCTIONS , L p UNIVERSALITY , AND PALEY - WIENER SPACES

Let ω be a regular measure on the unit circle and let p > 0. We establish asymptotic behavior, as n→∞, for the Lp Christoffel function λn,p (ω, z) = inf deg(P )≤n−1 ∫ π −π ∣∣P (eiθ)∣∣p dω (θ) |P (z)| at Lebesgue points z on the unit circle, where ω′ is lower semi-continuous. While bounds for these are classical, asymptotics have never been established for p 6= 2. The limit involves an extremal ...

A Note on Weighted Composition Operators on L^p-Spaces

A Note on Belief Structures and S-approximation Spaces

We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempsterchr('39')s multivalued mappings and lower and upper probabilities, and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory...

FUZZY HYPERVECTOR SPACES OVER VALUED FIELDS

In this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. Finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

ar X iv : 0 90 9 . 14 80 v 1 [ m at h . A P ] 8 S ep 2 00 9 ON QUASILINEAR PARABOLIC EVOLUTION EQUATIONS IN WEIGHTED L p - SPACES

In this paper we develop a geometric theory for quasilinear parabolic problems in weighted Lp-spaces. We prove existence and uniqueness of solutions as well as the continuous dependence on the initial data. Moreover, we make use of a regularization effect for quasilinear parabolic equations to study the ω-limit sets and the long-time behaviour of the solutions. These techniques are applied to a...