Essai sur les séries divergentes
Recently in this Journal J. Esterlé gave a new proof of the Wiener Tauberian theorem for using the Ahlfors-Heins theorem for bounded analytic functions on a half-plane. We here use essentially the same method to prove the analogous result for Beurling algebras . Our estimates need a theorem of Hayman and Korenblum.
We discuss the almost sure existence of random functions that can be written as sums of elementary pulses. We then estimate their uniform Hölder regularity by applying some results on coverings by random intervals.
In this article we introduce the convergence of extended realvalued double sequences [16], [17]. It is similar to our previous articles [15], [10]. In addition, we also prove Fatou’s lemma and the monotone convergence theorem for double sequences.
We show that the ideal of nowhere dense subsets of rationals cannot be extended to an analytic P-ideal, ideal nor maximal P-ideal. We also consider a problem of extendability to a non-meager P-ideals (in particular, to maximal P-ideals).