Geometry of polynomials:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
1966
|
| Edition: | Second edition |
| Series: | Mathematical Surveys
3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seiten 207 - 239.- 1. Auflage unter dem Titel: Marden, Morris: The geometry of the zeros of a polynomial in a complex variable |
| Physical Description: | XIII, 243 Seiten graph. Darst. |
Staff View
MARC
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| 100 | 1 | |a Marden, Morris |d 1905-1991 |e Verfasser |0 (DE-588)1112272038 |4 aut | |
| 245 | 1 | 0 | |a Geometry of polynomials |c by Morris Marden |
| 250 | |a Second edition | ||
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 1966 | |
| 300 | |a XIII, 243 Seiten |b graph. Darst. | ||
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| 490 | 1 | |a Mathematical Surveys |v 3 | |
| 500 | |a Literaturverzeichnis Seiten 207 - 239.- 1. Auflage unter dem Titel: Marden, Morris: The geometry of the zeros of a polynomial in a complex variable | ||
| 650 | 4 | |a Fonctions d'une variable complexe | |
| 650 | 4 | |a Polynômes | |
| 650 | 4 | |a Functions of complex variables | |
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Record in the Search Index
| _version_ | 1804116928454721536 |
|---|---|
| adam_text | TABLE OF CONTENTS
Prefaces vii
Abbreviations xiii
chapter i
Introduction
1. Some basic theorems 1
2. The zeros of the derivative 6
3. Physical interpretations 7
4. Geometric interpretation 9
5. Function theoretic interpretations. Infrapolynomials 13
chapter ii
The Critical Points of a Polynomial
6. The convex hull of critical points 21
7. The critical points of a real polynomial 25
8. Some generalizations 29
9. Polynomial solutions of Lame s differential equation 36
chapter hi
Invariantive Formulation
10. The derivative under linear transformations 43
11. Covariant force fields 45
12. Circular regions 48
13. Zeros of the polar derivative 49
14. Generalization to abstract spaces 55
chapter iv
Composite Polynomials
15. Apolar polynomials 60
16. Applications 65
17. Linear combinations of polynomials 74
18. Combinations of a polynomial and its derivatives 81
chapter v
The Critical Points of a Rational Function Which Has Its Zeros
and Poles in Prescribed Circular Regions
19. A two circle theorem for polynomials 89
20. Two circle theorems for rational functions 93
21. The general case 96
22. Some important special cases 102
v
vi TABLE OF CONTENTS
chapter vi
The Critical Points of a Polynomial Which
Has Only Some Prescribed Zeros
23. Polynomials with two given zeros 107
24. Mean Value Theorems 110
25. Polynomials with p known zeros 113
26. Alternative treatment 118
chapter vii
Bounds for the Zeros as Functions of All the Coefficients
27. The moduli of the zeros 122
28. The p zeros of smallest modulus 128
29. Refinement of the bounds 130
30. Applications 133
31. Matrix methods 139
CHAPTER VIII
Bounds for p Zeros as Functions of p + 1 Coefficients
32. Construction of bounds 147
33. Further bounds 151
34. Lacunary polynomials 156
35. Other bounds for lacunary polynomials 163
chapter ix
The Number of Zeros in a Half Plane or a Sector
36. Dynamic stability 166
37. Cauchy indices 168
38. Sturm sequences 171
39. Determinant sequences 174
40. The number of zeros with negative real parts 179
41. The number of zeros in a sector 189
chapter x
The Number of Zeros in a Given Circle
42. An algorithm 194
43. Determinant sequences 198
44. Polynomials with zeros on or symmetric in the unit circle 201
45. Singular determinant sequences 203
Bibliography 207
Index 241
|
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| author | Marden, Morris 1905-1991 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 517 - [Unassigned] |
| dewey-raw | 517.8 |
| dewey-search | 517.8 |
| dewey-sort | 3517.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV002526056 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:46:18Z |
| institution | BVB |
| language | English |
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| physical | XIII, 243 Seiten graph. Darst. |
| publishDate | 1966 |
| publishDateSearch | 1966 |
| publishDateSort | 1966 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical Surveys |
| series2 | Mathematical Surveys |
| spelling | Marden, Morris 1905-1991 Verfasser (DE-588)1112272038 aut Geometry of polynomials by Morris Marden Second edition Providence, RI American Mathematical Society 1966 XIII, 243 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical Surveys 3 Literaturverzeichnis Seiten 207 - 239.- 1. Auflage unter dem Titel: Marden, Morris: The geometry of the zeros of a polynomial in a complex variable Fonctions d'une variable complexe Polynômes Functions of complex variables Polynomials Polynom (DE-588)4046711-9 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 gnd rswk-swf Polynom (DE-588)4046711-9 s Geometrie (DE-588)4020236-7 s DE-604 Komplexe Variable (DE-588)4164905-9 s Mathematical Surveys 3 (DE-604)BV001888016 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001624754&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marden, Morris 1905-1991 Geometry of polynomials Mathematical Surveys Fonctions d'une variable complexe Polynômes Functions of complex variables Polynomials Polynom (DE-588)4046711-9 gnd Geometrie (DE-588)4020236-7 gnd Komplexe Variable (DE-588)4164905-9 gnd |
| subject_GND | (DE-588)4046711-9 (DE-588)4020236-7 (DE-588)4164905-9 |
| title | Geometry of polynomials |
| title_auth | Geometry of polynomials |
| title_exact_search | Geometry of polynomials |
| title_full | Geometry of polynomials by Morris Marden |
| title_fullStr | Geometry of polynomials by Morris Marden |
| title_full_unstemmed | Geometry of polynomials by Morris Marden |
| title_short | Geometry of polynomials |
| title_sort | geometry of polynomials |
| topic | Fonctions d'une variable complexe Polynômes Functions of complex variables Polynomials Polynom (DE-588)4046711-9 gnd Geometrie (DE-588)4020236-7 gnd Komplexe Variable (DE-588)4164905-9 gnd |
| topic_facet | Fonctions d'une variable complexe Polynômes Functions of complex variables Polynomials Polynom Geometrie Komplexe Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001624754&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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