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Conference papers
Square root singularities of infinite systems of functional equations
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 $\mathbf{y} (x)$.
Cited literature [18 references]
https://hal.inria.fr/hal-01185580
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Submitted on : Thursday, August 20, 2015 - 4:32:56 PM
Last modification on : Wednesday, October 13, 2021 - 7:58:04 PM
Long-term archiving on: : Wednesday, April 26, 2017 - 9:59:23 AM
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Thursday, August 20, 2015 - 4:32:56 PM
Last modification on : Wednesday, October 13, 2021 - 7:58:04 PM
Long-term archiving on: : Wednesday, April 26, 2017 - 9:59:23 AM
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