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Equivalences involving (p,q)-multi-norms

Oscar Blasco, H. G. Dales, Hung Le Pham (2014)

Studia Mathematica

We consider (p,q)-multi-norms and standard t-multi-norms based on Banach spaces of the form L r ( Ω ) , and resolve some question about the mutual equivalence of two such multi-norms. We introduce a new multi-norm, called the [p,q]-concave multi-norm, and relate it to the standard t-multi-norm.

Equivariant degree of convex-valued maps applied to set-valued BVP

Zdzisław Dzedzej (2012)

Open Mathematics

An equivariant degree is defined for equivariant completely continuous multivalued vector fields with compact convex values. Then it is applied to obtain a result on existence of solutions to a second order BVP for differential inclusions carrying some symmetries.

Equivariant Morse equation

Marcin Styborski (2012)

Open Mathematics

The paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by .x = −∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.

Ergodic averages with generalized weights

Doğan Çömez, Semyon N. Litvinov (2006)

Studia Mathematica

Two types of weighted ergodic averages are studied. It is shown that if F = {Fₙ} is an admissible superadditive process relative to a measure preserving transformation, then a Wiener-Wintner type result holds for F. Using this result new good classes of weights generated by such processes are obtained. We also introduce another class of weights via the group of unitary functions, and study the convergence of the corresponding weighted averages. The limits of such weighted averages are also identified....

Ergodic decomposition of quasi-invariant probability measures

Gernot Greschonig, Klaus Schmidt (2000)

Colloquium Mathematicae

The purpose of this note is to prove various versions of the ergodic decomposition theorem for probability measures on standard Borel spaces which are quasi-invariant under a Borel action of a locally compact second countable group or a discrete nonsingular equivalence relation. In the process we obtain a simultaneous ergodic decomposition of all quasi-invariant probability measures with a prescribed Radon-Nikodym derivative, analogous to classical results about decomposition of invariant probability...

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