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
Sätze vom Mazur-Orlicz-Typ
Schur΄s Theorem for Operators
Sčítání nekonečných řad pomocí integrálních transformací
Section of Euler summability method.
Sequence Spaces and Summability Factors.
Sequences of 0's and 1's
We investigate the extent to which sequence spaces are determined by the sequences of 0's and 1's that they contain.
Sequences of 0's and 1's: sequence spaces with the separable Hahn property
In [3] it was discovered that one of the main results in [1] (Theorem 5.2), applied to three spaces, contains a nontrivial gap in the argument, but neither the gap was closed nor a counterexample was provided. In [4] the authors verified that all three above mentioned applications of the theorem are true and stated a problem concerning the topological structure of one of these three spaces. In this paper we answer the problem and give a counterexample to the theorem in doubt. Also we establish a...
Sequences of Regular Summability Matrices.
Series like Taylor's series.
Series of iterates
Set-theoretic characteristics of summability of sequences and convergence of series