Unicity of Meromorphic Mappings:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
2003
|
| Schriftenreihe: | Advances in Complex Analysis and its Applications
1 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | For a given meromorphic function I(z) and an arbitrary value a, Nevanlinna's value distribution theory, which can be derived from the well known Poisson-Jensen formula, deals with relationships between the growth of the function and quantitative estimations of the roots of the equation: 1 (z) - a = O. In the 1920s as an application of the celebrated Nevanlinna's value distribution theory of meromorphic functions, R. Nevanlinna [188] himself proved that for two nonconstant meromorphic functions I, 9 and five distinctive values ai (i = 1,2,3,4,5) in the extended plane, if 1 1- (ai) = g-l(ai) 1M (ignoring multiplicities) for i = 1,2,3,4,5, then 1 = g. Furthermore 1, if 1- (ai) = g-l(ai) CM (counting multiplicities) for i = 1,2,3 and 4, then 1 = L(g), where L denotes a suitable Mobius transformation. Then in the 19708, F. Gross and C. C. Yang started to study the similar but more general questions of two functions that share sets of values. For instance, they proved that if 1 and 9 are two nonconstant entire functions and 8 , 82 and 83 are three distinctive finite sets such 1 1 that 1- (8 ) = g-1(8 ) CM for i = 1,2,3, then 1 = g |
| Beschreibung: | 1 Online-Ressource (IX, 467 p) |
| ISBN: | 9781475737752 9781441952431 |
| DOI: | 10.1007/978-1-4757-3775-2 |
Internformat
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| 245 | 1 | 0 | |a Unicity of Meromorphic Mappings |c by Pei-Chu Hu, Ping Li, Chung-Chun Yang |
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| 490 | 1 | |a Advances in Complex Analysis and its Applications |v 1 | |
| 500 | |a For a given meromorphic function I(z) and an arbitrary value a, Nevanlinna's value distribution theory, which can be derived from the well known Poisson-Jensen formula, deals with relationships between the growth of the function and quantitative estimations of the roots of the equation: 1 (z) - a = O. In the 1920s as an application of the celebrated Nevanlinna's value distribution theory of meromorphic functions, R. Nevanlinna [188] himself proved that for two nonconstant meromorphic functions I, 9 and five distinctive values ai (i = 1,2,3,4,5) in the extended plane, if 1 1- (ai) = g-l(ai) 1M (ignoring multiplicities) for i = 1,2,3,4,5, then 1 = g. Furthermore 1, if 1- (ai) = g-l(ai) CM (counting multiplicities) for i = 1,2,3 and 4, then 1 = L(g), where L denotes a suitable Mobius transformation. Then in the 19708, F. Gross and C. C. Yang started to study the similar but more general questions of two functions that share sets of values. For instance, they proved that if 1 and 9 are two nonconstant entire functions and 8 , 82 and 83 are three distinctive finite sets such 1 1 that 1- (8 ) = g-1(8 ) CM for i = 1,2,3, then 1 = g | ||
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Datensatz im Suchindex
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| author | Hu, Pei-Chu |
| author_facet | Hu, Pei-Chu |
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| author_sort | Hu, Pei-Chu |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.94 |
| dewey-search | 515.94 |
| dewey-sort | 3515.94 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-3775-2 |
| format | Electronic eBook |
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| id | DE-604.BV042421523 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475737752 9781441952431 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856940 |
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| publishDate | 2003 |
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| publisher | Springer US |
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| series | Advances in Complex Analysis and its Applications |
| series2 | Advances in Complex Analysis and its Applications |
| spelling | Hu, Pei-Chu Verfasser aut Unicity of Meromorphic Mappings by Pei-Chu Hu, Ping Li, Chung-Chun Yang Boston, MA Springer US 2003 1 Online-Ressource (IX, 467 p) txt rdacontent c rdamedia cr rdacarrier Advances in Complex Analysis and its Applications 1 For a given meromorphic function I(z) and an arbitrary value a, Nevanlinna's value distribution theory, which can be derived from the well known Poisson-Jensen formula, deals with relationships between the growth of the function and quantitative estimations of the roots of the equation: 1 (z) - a = O. In the 1920s as an application of the celebrated Nevanlinna's value distribution theory of meromorphic functions, R. Nevanlinna [188] himself proved that for two nonconstant meromorphic functions I, 9 and five distinctive values ai (i = 1,2,3,4,5) in the extended plane, if 1 1- (ai) = g-l(ai) 1M (ignoring multiplicities) for i = 1,2,3,4,5, then 1 = g. Furthermore 1, if 1- (ai) = g-l(ai) CM (counting multiplicities) for i = 1,2,3 and 4, then 1 = L(g), where L denotes a suitable Mobius transformation. Then in the 19708, F. Gross and C. C. Yang started to study the similar but more general questions of two functions that share sets of values. For instance, they proved that if 1 and 9 are two nonconstant entire functions and 8 , 82 and 83 are three distinctive finite sets such 1 1 that 1- (8 ) = g-1(8 ) CM for i = 1,2,3, then 1 = g Mathematics Field theory (Physics) Functions of complex variables Global analysis Differential equations, partial Several Complex Variables and Analytic Spaces Functions of a Complex Variable Global Analysis and Analysis on Manifolds Field Theory and Polynomials Mathematik Li, Ping Sonstige oth Yang, Chung-Chun Sonstige oth Advances in Complex Analysis and its Applications 1 (DE-604)BV021550762 1 https://doi.org/10.1007/978-1-4757-3775-2 Verlag Volltext |
| spellingShingle | Hu, Pei-Chu Unicity of Meromorphic Mappings Advances in Complex Analysis and its Applications Mathematics Field theory (Physics) Functions of complex variables Global analysis Differential equations, partial Several Complex Variables and Analytic Spaces Functions of a Complex Variable Global Analysis and Analysis on Manifolds Field Theory and Polynomials Mathematik |
| title | Unicity of Meromorphic Mappings |
| title_auth | Unicity of Meromorphic Mappings |
| title_exact_search | Unicity of Meromorphic Mappings |
| title_full | Unicity of Meromorphic Mappings by Pei-Chu Hu, Ping Li, Chung-Chun Yang |
| title_fullStr | Unicity of Meromorphic Mappings by Pei-Chu Hu, Ping Li, Chung-Chun Yang |
| title_full_unstemmed | Unicity of Meromorphic Mappings by Pei-Chu Hu, Ping Li, Chung-Chun Yang |
| title_short | Unicity of Meromorphic Mappings |
| title_sort | unicity of meromorphic mappings |
| topic | Mathematics Field theory (Physics) Functions of complex variables Global analysis Differential equations, partial Several Complex Variables and Analytic Spaces Functions of a Complex Variable Global Analysis and Analysis on Manifolds Field Theory and Polynomials Mathematik |
| topic_facet | Mathematics Field theory (Physics) Functions of complex variables Global analysis Differential equations, partial Several Complex Variables and Analytic Spaces Functions of a Complex Variable Global Analysis and Analysis on Manifolds Field Theory and Polynomials Mathematik |
| url | https://doi.org/10.1007/978-1-4757-3775-2 |
| volume_link | (DE-604)BV021550762 |
| work_keys_str_mv | AT hupeichu unicityofmeromorphicmappings AT liping unicityofmeromorphicmappings AT yangchungchun unicityofmeromorphicmappings |