Geodesic
On the convergence of polynomial Fredholm series
Dalʹnevostočnyj matematičeskij žurnal, Tome 9 (2009) no. 1, pp. 131-139 
I. M. Novitskii. On the convergence of polynomial Fredholm series. Dalʹnevostočnyj matematičeskij žurnal, Tome 9 (2009) no. 1, pp. 131-139. http://geodesic.mathdoc.fr/item/DVMG_2009_9_1_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this note, we study the infinite system of Fredholm series of polynomials in $\lambda$, formed, in the classical way, for a kernel on $\mathbb{R}^2$ of the form $\boldsymbol{H}(s,t)-\lambda\boldsymbol{S}(s,t)$, where $\lambda$ is a complex parameter. We establish a convergence of these series in the complex plane with respect to sup-norms of various spaces of continuous functions. The convergence results apply to solving a Fredholm integral equation with a kernel that is linear with respect to parameter.

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