Abstract
The aim of this work is to investigate the geometric functions theory of plane domains, which are complements of finite unions of intervals. Our primary goal was the computation of the capacity of a finite union of intervals. We show that the spectral curve, given by the Burchnall–Chaundy theory for commuting differences operators and hyperelliptic theta functions play a chief role. This is the first of two papers devoted to this subject.
Dedicated to Professor Daniel Alpay on the occasion of his 60th birthday
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Sebbar, A. (2017). Finite Unions of Intervals, Part I. In: Colombo, F., Sabadini, I., Struppa, D., Vajiac, M. (eds) Advances in Complex Analysis and Operator Theory. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-62362-7_12
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DOI: https://doi.org/10.1007/978-3-319-62362-7_12
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-62361-0
Online ISBN: 978-3-319-62362-7
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