Let Ω be a domain in the complex plane bounded by m+1 disjoint, analytic simple closed curves and let be n+1 distinct points in Ω. We show that for each (n+1)-tuple of complex numbers, there is a unique analytic function B such that: (a) B is continuous on the closure of Ω and has constant modulus on each component of the boundary of Ω; (b) B has n or fewer zeros in Ω; and (c) , 0 ≤ j ≤ n.
@article{bwmeta1.element.bwnjournal-article-smv103i3p265bwm,
author = {Stephen Fisher},
title = {Pick-Nevanlinna interpolation on finitely-connected domains},
journal = {Studia Mathematica},
volume = {103},
year = {1992},
pages = {265-273},
zbl = {0810.30027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv103i3p265bwm}
}
Fisher, Stephen. Pick-Nevanlinna interpolation on finitely-connected domains. Studia Mathematica, Tome 103 (1992) pp. 265-273. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv103i3p265bwm/
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