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.
Url:
DOI: 10.1007/978-1-4757-2956-6_6
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 001856
- to stream Istex, to step Curation: 001856
- to stream Istex, to step Checkpoint: 001619
Links to Exploration step
ISTEX:780D91377114E149F6F6FAB9F0387CBDE1CD0278Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Functions with Prescribed Principal Parts</title>
<author><name sortKey="Remmert, Reinhold" sort="Remmert, Reinhold" uniqKey="Remmert R" first="Reinhold" last="Remmert">Reinhold Remmert</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:780D91377114E149F6F6FAB9F0387CBDE1CD0278</idno>
<date when="1998" year="1998">1998</date>
<idno type="doi">10.1007/978-1-4757-2956-6_6</idno>
<idno type="url">https://api.istex.fr/document/780D91377114E149F6F6FAB9F0387CBDE1CD0278/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">001856</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001856</idno>
<idno type="wicri:Area/Istex/Curation">001856</idno>
<idno type="wicri:Area/Istex/Checkpoint">001619</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">001619</idno>
<idno type="wicri:doubleKey">0072-5285:1998:Remmert R:functions:with:prescribed</idno>
<idno type="wicri:Area/Main/Merge">001780</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Functions with Prescribed Principal Parts</title>
<author><name sortKey="Remmert, Reinhold" sort="Remmert, Reinhold" uniqKey="Remmert R" first="Reinhold" last="Remmert">Reinhold Remmert</name>
<affiliation wicri:level="3"><country xml:lang="fr">Allemagne</country>
<wicri:regionArea>Mathematisches Institut, Westfälische Wilhelms—Universität Münster, Einsteinstrasse 62, D-48149, Münster</wicri:regionArea>
<placeName><region type="land" nuts="1">Rhénanie-du-Nord-Westphalie</region>
<region type="district" nuts="2">District de Münster</region>
<settlement type="city">Münster</settlement>
</placeName>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="s">Graduate Texts in Mathematics</title>
<imprint><date>1998</date>
</imprint>
<idno type="ISSN">0072-5285</idno>
<idno type="ISSN">0072-5285</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">0072-5285</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">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.</div>
</front>
</TEI>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Merge
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001780 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Merge/biblio.hfd -nk 001780 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Mathematiques |area= BourbakiV1 |flux= Main |étape= Merge |type= RBID |clé= ISTEX:780D91377114E149F6F6FAB9F0387CBDE1CD0278 |texte= Functions with Prescribed Principal Parts }}
![]() | This area was generated with Dilib version V0.6.33. | ![]() |