Functions with Prescribed Principal Parts
Identifieur interne : 001780 ( Main/Merge ); précédent : 001779; suivant : 001781Functions with Prescribed Principal Parts
Auteurs : Reinhold Remmert [Allemagne]Source :
- Graduate Texts in Mathematics [ 0072-5285 ] ; 1998.
Abstract
Abstract: If h is meromorphic in the region D, its pole setP(h) is locally finite in D. By the existence theorem 4.1.5, every set that is locally finite in D is the pole set of some function h ∈ M(D) (see also 3.1.5(1)). We now pose the following problem: Let T = {d1, d2, ...} be a set that is locally finite in D, and let every point d v ∈ T be somehow assigned a “ finite principal part” $${q_v}\left( z \right) = \sum\nolimits_{u = 1}^{mv} {avu} {\left( {z - {d_v}} \right)^{ - u}} \ne 0$$ . Construct a function meromorphic in D that has T as its pole set and moreover has principal part q v at each point d v.
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DOI: 10.1007/978-1-4757-2956-6_6
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