An Extension of Cauchy's Criterion to Nörlund Summability.
An ordered set of Nörlund means.
Application of a Tauberian theorem to finite model theory.
Approximation by Abel means and Tauberian Theorems in sequences spaces
Axiomatic theory of divergent series and cohomological equations
A general theory of summation of divergent series based on the Hardy-Kolmogorov axioms is developed. A class of functional series is investigated by means of ergodic theory. The results are formulated in terms of solvability of some cohomological equations, all solutions to which are nonmeasurable. In particular, this realizes a construction of a nonmeasurable function as first conjectured by Kolmogorov.
Boundary behavior and Cesàro means of universal Taylor series.
We study boundary properties of universal Taylor series. We prove that if f is a universal Taylor series on the open unit disk, then there exists a residual subset G of the unit circle such that f is unbounded on all radii with endpoints in G. We also study the effect of summability methods on universal Taylor series. In particular, we show that a Taylor series is universal if and only if its Cesàro means are universal.
Bounded variation sequences of order k and the representation of null sequences.
Boundness of Cesàro means operators.
Cesàro statistical core of complex number sequences.
Cesàro summability factors and a comparison of convergence rates
Characterization for relations on some summability methods.
Charakterisierungen für Hausdorff-Matrizen.
Criteria for membership of the Besov spaces BS pq.
Die allgemeine Form der O-Tauber-Bedingung für das Euler-Knopp- und Borel-Verfahren.
Differential transforms of Cesàro averages in weighted spaces .
Distributional asymptotic expansions of spectral functions and of the associated Green kernels.
Distributional versions of Littlewood's Tauberian theorem
We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness, while the second type imposes a one-sided assumption on the Cesàro behavior of the distribution. We apply these Tauberian results to deduce a number of Tauberian theorems for power series and Stieltjes integrals where Cesàro summability follows from Abel...
Equiconvergence and equisummability of Jacobi series
2010 Mathematics Subject Classification: 33C45, 40G05.In this paper we give some results concerning the equiconvergence and equisummability of series in Jacobi polynomials.
Euler-Summierbarkeit konform-äquivalenter Reihen.
General Nörlund transforms and power series methods.