Square root singularities of infinite systems of functional equations

Johannes F. Morgenbesser 1
1 Institut für Diskrete Mathematik und Geometrie [Wien]
Abstract : Infinite systems of equations appear naturally in combinatorial counting problems. Formally, we consider functional equations of the form $\mathbf{y} (x)=F(x,\mathbf{y} (x))$, where $F(x,\mathbf{y} ):\mathbb{C} \times \ell^p \to \ell^p$ is a positive and nonlinear function, and analyze the behavior of the solution $\mathbf{y} (x)$ at the boundary of the domain of convergence. In contrast to the finite dimensional case different types of singularities are possible. We show that if the Jacobian operator of the function $F$ is compact, then the occurring singularities are of square root type, as it is in the finite dimensional setting. This leads to asymptotic expansions of the Taylor coefficients of $\mathbf{y} (x)$.
Keywords : generating function functional equation compact operator Krein-Rutman theorem infinite matrices
Type de document :
Communication dans un congrès
Drmota, Michael and Gittenberger, Bernhard. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pp.513-526, 2010, DMTCS Proceedings
Liste complète des métadonnées

Littérature citée [18 références]  Voir  Masquer  Télécharger
https://hal.inria.fr/hal-01185580
Contributeur : Coordination Episciences Iam <>
Soumis le : jeudi 20 août 2015 - 16:32:56
Dernière modification le : mardi 7 mars 2017 - 15:07:36
Document(s) archivé(s) le : mercredi 26 avril 2017 - 09:59:23

Fichier

dmAM0136.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

  • HAL Id : hal-01185580, version 1

Collections

INSMI | TDS-MACS

Citation

Johannes F. Morgenbesser. Square root singularities of infinite systems of functional equations. Drmota, Michael and Gittenberger, Bernhard. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pp.513-526, 2010, DMTCS Proceedings. 〈hal-01185580〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

47

Téléchargements de fichiers

96

Contact


archive-ouverte@inria.fr