Unicity of Meromorphic Mappings:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Springer US
2003
|
| Series: | Advances in Complex Analysis and its Applications
1 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 |
| Physical Description: | 1 Online-Ressource (IX, 467 p) |
| ISBN: | 9781475737752 9781441952431 |
| DOI: | 10.1007/978-1-4757-3775-2 |
Staff View
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042421523 | ||
| 003 | DE-604 | ||
| 005 | 20180111 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2003 |||| o||u| ||||||eng d | ||
| 020 | |a 9781475737752 |c Online |9 978-1-4757-3775-2 | ||
| 020 | |a 9781441952431 |c Print |9 978-1-4419-5243-1 | ||
| 024 | 7 | |a 10.1007/978-1-4757-3775-2 |2 doi | |
| 035 | |a (OCoLC)864045624 | ||
| 035 | |a (DE-599)BVBBV042421523 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515.94 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Hu, Pei-Chu |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Unicity of Meromorphic Mappings |c by Pei-Chu Hu, Ping Li, Chung-Chun Yang |
| 264 | 1 | |a Boston, MA |b Springer US |c 2003 | |
| 300 | |a 1 Online-Ressource (IX, 467 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 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 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Field theory (Physics) | |
| 650 | 4 | |a Functions of complex variables | |
| 650 | 4 | |a Global analysis | |
| 650 | 4 | |a Differential equations, partial | |
| 650 | 4 | |a Several Complex Variables and Analytic Spaces | |
| 650 | 4 | |a Functions of a Complex Variable | |
| 650 | 4 | |a Global Analysis and Analysis on Manifolds | |
| 650 | 4 | |a Field Theory and Polynomials | |
| 650 | 4 | |a Mathematik | |
| 700 | 1 | |a Li, Ping |e Sonstige |4 oth | |
| 700 | 1 | |a Yang, Chung-Chun |e Sonstige |4 oth | |
| 830 | 0 | |a Advances in Complex Analysis and its Applications |v 1 |w (DE-604)BV021550762 |9 1 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4757-3775-2 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027856940 | ||
Record in the Search Index
| _version_ | 1804153094697648128 |
|---|---|
| any_adam_object | |
| author | Hu, Pei-Chu |
| author_facet | Hu, Pei-Chu |
| author_role | aut |
| author_sort | Hu, Pei-Chu |
| author_variant | p c h pch |
| building | Verbundindex |
| bvnumber | BV042421523 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)864045624 (DE-599)BVBBV042421523 |
| dewey-full | 515.94 |
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02927nmm a2200517zcb4500</leader><controlfield tag="001">BV042421523</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180111 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2003 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781475737752</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4757-3775-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781441952431</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4419-5243-1</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4757-3775-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)864045624</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042421523</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.94</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hu, Pei-Chu</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Unicity of Meromorphic Mappings</subfield><subfield code="c">by Pei-Chu Hu, Ping Li, Chung-Chun Yang</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston, MA</subfield><subfield code="b">Springer US</subfield><subfield code="c">2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (IX, 467 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Advances in Complex Analysis and its Applications</subfield><subfield code="v">1</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Field theory (Physics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functions of complex variables</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Global analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, partial</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Several Complex Variables and Analytic Spaces</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functions of a Complex Variable</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Global Analysis and Analysis on Manifolds</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Field Theory and Polynomials</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Li, Ping</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Yang, Chung-Chun</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Advances in Complex Analysis and its Applications</subfield><subfield code="v">1</subfield><subfield code="w">(DE-604)BV021550762</subfield><subfield code="9">1</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4757-3775-2</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027856940</subfield></datafield></record></collection> |
| 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 |
| oclc_num | 864045624 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (IX, 467 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer US |
| record_format | marc |
| 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 |