Functions with Prescribed Principal Parts

  • Reinhold Remmert
Part of the Graduate Texts in Mathematics book series (GTM, volume 172)

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 vT 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.

Keywords

Holomorphic Function Meromorphic Function Ideal Theory Principal Part Principal Ideal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Reinhold Remmert
    • 1
  1. 1.Mathematisches InstitutWestfälische Wilhelms—Universität MünsterMünsterGermany

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