Viktor Losert

Dynamics of games and genes: Discrete versus continuous time

It is shown that in the classical model of population genetics (Fisher-Wright-Haldane, discrete or continuous version) every solution p(t) converges to equilibrium for t → ∞. For related models of evolutionary games (with non-symmetric matrices) it is shown that the transformation that describes the dynamics is a diffeomorphism (in particular one-to-one).

Evolutionary Dynamics of zero-sum games

Aim model in terms of differential equations is used to explain mammalian ovulation control, in particular regulation for a prescribed number of mature eggs.

The norm-strict bidual of a Banach algebra and the dual of Cu(G)

To each Banach algebra A we associate a (generally) larger Banach algebra A+ which is a quotient of its bidual A″. It can be constructed using the strict topology on A and the Arens product on A″. A+ has certain more pleasant properties than A″, e.g. if A has a bounded right approximate identity, then A+ has a two-sided unit. In the special case A=L1(G) (G a locally compact abelian group) one gets A+=Cu(G)′, the dual of the space of bounded, uniformly continuous functions on G, and we show that the center of the convolution algebra Cu(G)′ is precisely the space M(G) of finite measures on G.

The strong sweeping out property for lacunary sequences, Riemann sums, convolution powers, and related matters

In this paper we establish conditions on a sequence of operators which imply divergence. In fact, we give conditions which imply that we can find a set B of measure as close to zero as we like, but such that the operators applied to the characteristic function of this set have a lim sup equal to 1 and a lim inf equal to 0 a.e. (strong sweeping out). The results include the fact that ergodic averages along lacunary sequences, certain convolution powers, and the Riemann sums considered by Rudin are all strong sweeping out. One of the criteria for strong sweeping out involves a condition on the Fourier transform of the sequence of measures, which is often easily checked. The second criterion for strong sweeping out involves showing that a sequence of numbers satisfies a property similar to the conclusion of Kroneckers lemma on sequences linearly independent over the rationals.

The centre of the second conjugate algebra of the Fourier algebra for infinite products of groups

In this paper, we shall prove that if

On the Existence of Uniformly Distributed Sequences in Compact Topological Spaces II.

G

Ergodic sequences in the Fourier-Stieltjes algebra and measure algebra of a locally compact group

is a countably infinite product of second countable amenable locally compact groups

Almost constant sequences of transformations

G_i,i\,{=}\,0,1,2,\dots

Proof of the Ghahramani–Lau conjecture

and each

The Borel Property for Simple Riesz Means

G_i