Remark on the convergence of the sequences defined by certain difference equations
Remarks on a moment problem and a problem of perfection of power methods of limitation
Remarks on a paper of S. K. Bhattacharyya and B. K. Lahiri
Remarks on duality for -groups. I. Products and coproducts
Remarks on several types of convergence of bounded sequences
In this paper we analyze relations among several types of convergences of bounded sequences, in particulars among statistical convergence, -convergence, -convergence, almost convergence, strong -Cesàro convergence and uniformly strong -Cesàro convergence.
Remarks on statistical and -convergence of series
In this paper we investigate the relationship between the statistical (or generally -convergence) of a series and the usual convergence of its subseries. We also give a counterexample which shows that Theorem 1 of the paper by B. C. Tripathy “On statistically convergent series”, Punjab. Univ. J. Math. 32 (1999), 1–8, is not correct.
Remarque sur le cas douteux relatif à certains caractères de convergence des séries
Remarques sur divers articles, concernant la théorie des séries
Repeated convergence and fractional differences
Repeated Modifications of Limit k-Periodic continued Fractions.
Resommation des series formelles. Solutions d'équations différentielles linéaires ordinaires du second ordre dans le champ complexe au voisinage de singularités irrégulières.
Results on spline-Fourier and Ciesielski-Fourier series
Some recent results on spline-Fourier and Ciesielski-Fourier series are summarized. The convergence of spline Fourier series and the basis properties of the spline systems are considered. Some classical topics, that are well known for trigonometric and Walsh-Fourier series, are investigated for Ciesielski-Fourier series, such as inequalities for the Fourier coefficients, convergence a.e. and in norm, Fejér and θ-summability, strong summability and multipliers. The connection between Fourier series...
Resurgence of the Kontsevich-Zagier series
The paper is concerned with the resurgence of the Kontsevich-Zagier seriesWe give an explicit formula for the Borel transform of the power series when from which its analytic continuation, its singularities (all on the positive real axis) and the local monodromy can be manifestly determined. We also give two formulas (one involving the Dedekind eta function, and another involving the complex error function) for the right, left and median summation of the Borel transform. We also prove that the...
Résurgence paramétrique et exponentielle petitesse de l'écart des séparatrices du pendule rapidement forcé
Henri Poincaré avait déjà remarqué que les variétés stable et instable du pendule perturbé, défini par l’hamiltonienne coïncident pas lorsque que le paramètre n’est pas nul, mais qu’on peut leur associer un même développement formel divergent en puissance de . Cette divergence est ici analysée au moyen de la récente théorie de la résurgence, et du calcul étranger qui permet de trouver un équivalent asymptotique de l’écart des deux variétés pour tendant vers zéro - du moins cela est-il montré...
Résurgence quantique