Introduction to the classical theory of Abelian functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
1992
|
| Series: | Translations of Mathematical Monographs
96 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russischen übersetzt |
| Physical Description: | VIII, 175 Seiten |
| ISBN: | 082184542X |
Staff View
MARC
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| 240 | 1 | 0 | |a Vvedenie v klassičeskuju teoriju abelevych funkcij |
| 245 | 1 | 0 | |a Introduction to the classical theory of Abelian functions |c A. I. Markushevich |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 1992 | |
| 300 | |a VIII, 175 Seiten | ||
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Record in the Search Index
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| adam_text | Contents
Preface vii
CHAPTER I. Historical introduction. The Jacobi inversion problem 1
§1. Euler s equation 1
§2. Elliptic functions of Gauss 4
§3. Jacobi s inversion method 8
§4. Jacobi identities 12
§5. Problem of inversion of a hyperelliptic integral 17
§6. Problem of Jacobi. Gopel and Rosenhain 23
§7. Algebraic functions and their Riemann surfaces 27
§8. Abelian integrals. Abel s theorem 31
§9. Main directions of development of the theory of Abelian
functions 40
CHAPTER II. Periodic functions of several complex variables 45
§ 1. Divisibility relation for functions analytic at a point 45
§2. Entire and meromorphic functions 48
§3. The set of periods. Infinitesimal periods 51
§4. Conditions for independence of periods 55
§5. The fundamental system of periods 59
§6. Transformation of period matrix 63
§7. Generalized Fourier series of a periodic entire function 65
§8. Construction of an entire function of one variable from its
difference 69
CHAPTER III. Riemann matrices. Jacobian (intermediate) functions 73
§1. Riemann matrices. Elementary conditions 73
§2. The first system of difference equations. Conditions of
solvability 77
§3. Construction of the solution of the first system 81
§4. Jacobian or intermediate functions. The second system of
difference equations 85
§5. Solvability conditions for the second system and the solution of
the second system 92
V
vi CONTENTS
§6. First and second period matrices. The characteristic matrix N 96
§7. Upper bound on absolute values of Jacobian functions.
Riemann inequality 100
§8. Statement of necessary and sufficient conditions for a Riemann
matrix. The principal matrix 107
CHAPTER IV. Construction of Jacobian functions of a given type.
Theta functions and Abelian functions. Abelian and
Picard manifolds 115
§1. Construction of the characteristic matrix N and the second
period matrix A, using given Q and P 115
§2. Construction of Jacobian functions of a given type. Theta
functions 119
§3. Construction of Abelian functions. Fields of Abelian functions 127
§4. Theta functions with characteristics 134
§5. Weierstrass Poincare theorem 140
§6. Abelian and Picard manifolds 145
§7. Rational functions on Picard varieties. Picard integrals of the
first kind. 148
Appendix A. Skew symmetric determinants 153
Appendix B. Divisors of analytic functions 159
Appendix C. A summary of the most important formulas 172
|
| any_adam_object | 1 |
| author | Markuševič, Aleksej Ivanovič 1908-1979 |
| author_GND | (DE-588)133996859 |
| author_facet | Markuševič, Aleksej Ivanovič 1908-1979 |
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| author_sort | Markuševič, Aleksej Ivanovič 1908-1979 |
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| building | Verbundindex |
| bvnumber | BV005457906 |
| classification_rvk | SK 750 SK 680 |
| ctrlnum | (OCoLC)246828174 (DE-599)BVBBV005457906 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV005457906 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:29:52Z |
| institution | BVB |
| isbn | 082184542X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003415346 |
| oclc_num | 246828174 |
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| owner | DE-384 DE-355 DE-BY-UBR DE-824 DE-188 |
| owner_facet | DE-384 DE-355 DE-BY-UBR DE-824 DE-188 |
| physical | VIII, 175 Seiten |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Translations of Mathematical Monographs |
| series2 | Translations of Mathematical Monographs |
| spelling | Markuševič, Aleksej Ivanovič 1908-1979 Verfasser (DE-588)133996859 aut Vvedenie v klassičeskuju teoriju abelevych funkcij Introduction to the classical theory of Abelian functions A. I. Markushevich Providence, RI American Mathematical Society 1992 VIII, 175 Seiten txt rdacontent n rdamedia nc rdacarrier Translations of Mathematical Monographs 96 Aus dem Russischen übersetzt Abelsche Funktion (DE-588)4140987-5 gnd rswk-swf Abelsche Funktion (DE-588)4140987-5 s DE-604 Translations of Mathematical Monographs 96 (DE-604)BV000002394 96 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003415346&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Markuševič, Aleksej Ivanovič 1908-1979 Introduction to the classical theory of Abelian functions Translations of Mathematical Monographs Abelsche Funktion (DE-588)4140987-5 gnd |
| subject_GND | (DE-588)4140987-5 |
| title | Introduction to the classical theory of Abelian functions |
| title_alt | Vvedenie v klassičeskuju teoriju abelevych funkcij |
| title_auth | Introduction to the classical theory of Abelian functions |
| title_exact_search | Introduction to the classical theory of Abelian functions |
| title_full | Introduction to the classical theory of Abelian functions A. I. Markushevich |
| title_fullStr | Introduction to the classical theory of Abelian functions A. I. Markushevich |
| title_full_unstemmed | Introduction to the classical theory of Abelian functions A. I. Markushevich |
| title_short | Introduction to the classical theory of Abelian functions |
| title_sort | introduction to the classical theory of abelian functions |
| topic | Abelsche Funktion (DE-588)4140987-5 gnd |
| topic_facet | Abelsche Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003415346&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT markusevicaleksejivanovic vvedenievklassiceskujuteorijuabelevychfunkcij AT markusevicaleksejivanovic introductiontotheclassicaltheoryofabelianfunctions |