On almost everywhere convergence of orthogonal spline projections with arbitrary knots

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...

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.

Almost Everywhere Convergence of Poisson Integrals on Generalized Half-planes

On Almost Everywhere Strong Convergence of Multidimensional Continued Fraction Algorithms

We describe a strategy which allows one to produce computer assisted proofs of almost everywhere strong convergence of Jacobi-Perron type algorithms in arbitrary dimension. Numerical work is carried out in dimension three to illustrate our method. To the best of our knowledge this is the rst result on almost everywhere strong convergence in dimension greater than two.

Almost Everywhere Convergence in Family of IF-events With Product

The aim of this paper is to define the lower and upper limits on the family of IF-events with product. We compare two concepts of almost everywhere convergence and we show that they are equivalent, too.