Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere

Dynamics of nonautonomous tridiagonal competitive-cooperative systems of differential equations

Skew-product flow which is generated by a nonautonomous recurrent tridiagonal competitive-cooperative system of differential equations is considered. It is shown that any minimal set is an almost 1-1 extension of the base flow and any ω-limit set contains at most two minimal sets, which generalizes the results of J. Smillie [SIAM J. Math. Anal., 15(1984), pp. 530–534] in autonomous cases and H....

Almost Everywhere Convergence of Series in L

We answer positively a question of J. Rosenblatt (1988), proving the existence of a sequence (ci) with ∑∞ i=1 |ci| = ∞, such that for every dynamical system (X,Σ, m, T ) and f ∈ L1(X), ∑∞i=1 cif(T ix) converges almost everywhere. A similar result is obtained in the real variable context.

Value indefinite observables are almost everywhere

Value indefinite observables are almost everywhere Alastair A. Abbott, 2, ∗ Cristian S. Calude, † and Karl Svozil 1, ‡ Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, New Zealand Centre Cavaillès, CIRPHLES, École Normale Supérieure, 29 rue d’Ulm, 75005 Paris, France Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10...

Almost Everywhere Convergence of Poisson Integrals on Generalized Half-planes

Almost Everywhere Convergence of Orthogonal Expansions of Several Variables

For weighted L space on the unit sphere of R, in which the weight functions are invariant under finite reflection groups, a maximal function is introduced and used to prove the almost everywhere convergence of orthogonal expansions in h-harmonics. The result applies to various methods of summability, including the de la Vallée Poussin means and the Cesàro means. Similar results are also establi...