Johannes F. Morgenbesser - Square root singularities of infinite systems of functional equations

dmtcs:2782 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) - https://doi.org/10.46298/dmtcs.2782
Square root singularities of infinite systems of functional equationsConference paper

Authors: Johannes F. Morgenbesser 1

  • 1 Institut für Diskrete Mathematik und Geometrie [Wien]

Infinite systems of equations appear naturally in combinatorial counting problems. Formally, we consider functional equations of the form y(x)=F(x,y(x)), where F(x,y):C×pp is a positive and nonlinear function, and analyze the behavior of the solution 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 y(x).


Volume: DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: functional equation,compact operator,Krein-Rutman theorem,infinite matrices,generating function,[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]

2 Documents citing this article

Consultation statistics

This page has been seen 297 times.
This article's PDF has been downloaded 1009 times.