A second course in complex analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
W. A. Benjamin
1967
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 246 Seiten graph. Darst. |
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| 245 | 1 | 0 | |a A second course in complex analysis |c William A. Veech, University of California, Berkeley |
| 264 | 1 | |a New York, NY [u.a.] |b W. A. Benjamin |c 1967 | |
| 300 | |a IX, 246 Seiten |b graph. Darst. | ||
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PREFACE
CHAPTER 1 ANALYTIC CONTINUATION 1
1. THE EXPONENTIAL FUNCTION AND THE LOGARITHM 1
2. CONTINUATION SEQUENCES 11
3. CONTINUATION ALONG AN ARC 13
4. GERMS 17
5. EXISTENCE OF CONTINUATIONS 19
6. THE WINDING NUMBER 23
7. THE ARGUMENT PRINCIPLE 27
8. THE MONODROMY THEOREM 33
9. COMPOSITION OF GERMS 36
10. COMPOSITION OF CONTINUATIONS 38
11. COVERING SURFACES 40
CHAPTER 2 GEOMETRIC CONSIDERATIONS 45
1. COMPLEX PROJECTIVE SPACE 45
2. LINEAR TRANSFORMATIONS 48
3. FRACTIONAL LINEAR TRANSFORMATIONS 51
4. PROPERTIES OF FRACTIONAL LINEAR
TRANSFORMATIONS 53
5. SYMMETRY 58
6. SCHWARZ S LEMMA 61
7. NON EUCLIDEAN GEOMETRY 69
8. THE SCHWARZ REFLECTION PRINCIPLE 75
CHAPTER 3 THE MAPPING THEOREMS OF RIEMANN
AND KOEBE 82
1. ANALYTIC EQUIVALENCE 82
2. LOCAL UNIFORM CONVERGENCE 85
Mi
viii Contents
3. a theorem of hurwitz 89
4. implications of pointwise convergence 92
5. implications of convergence on a subset 95
6. approximately linear functions—another appli¬
cation of schwarz s lemma 99
7. a uniformization theorem 103
8. a closer look at the covering 111
9. boundary behavior 112
10. lindelof s lemma 113
11. facts from topology 116
12. continuity at the boundary 117
13. a theorem of fejer 121
CHAPTER 4 THE MODULAR FUNCTION 126
1. exceptional values 126
2. the modular configuration 128
3. the landau radius 133
4. schottky s theorem 135
5. normal families 137
6. montel s theorem 142
7. picard s second theorem 144
8. the koebe faber distortion theorem 145
9. bloch s theorem 149
CHAPTER 5 THE HADAMARD PRODUCT THEOREM 152
1. INFINITE PRODUCTS 152
2. PRODUCTS OF FUNCTIONS 162
3. THE WEIERSTRASS PRODUCT THEOREM 165
4. FUNCTIONS OF FINITE ORDER 170
5. EXPONENT OF CONVERGENCE 174
6. CANONICAL PRODUCTS 178
7. THE BOREL CARATHEODORY LEMMA ANOTHER FORM OF
SCHWARZ S LEMMA 181
8. A LEMMA OF H. CARTAN 184
9. THE HADAMARD PRODUCT THEOREM 186
10. THE GAMMA FUNCTION 190
11. STANDARD FORMULAS 193
12. THE INTEGRAL REPRESENTATION OF Y{z) 195
Contents ix
CHAPTER 6 THE PRIME NUMBER THEOREM 200
1. DIRICHLET SERIES 200
2. NUMBER THEORETIC FUNCTIONS 202
3. STATEMENT OF THE PRIME NUMBER THEOREM 205
4. THE RIEMANN ZETA FUNCTION 210
5. ANALYTIC CONTINUATION OF f (s) 213
6. riemann s functional equation 219
7. the zeros of f (s) in the critical strip 222
8. f (s) for Re s = 1 227
9. INTEGRAL REPRESENTATION OF DIRICHLET SERIES 229
10. INTEGRAL THEORETIC LEMMAS 232
11. WEAK LIMITS 235
12. A TAUBERIAN THEOREM 238
BIBLIOGRAPHY 243
INDEX 245
|
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| language | English |
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| publishDate | 1967 |
| publishDateSearch | 1967 |
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| publisher | W. A. Benjamin |
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| spelling | Veech, William A. Verfasser aut A second course in complex analysis William A. Veech, University of California, Berkeley New York, NY [u.a.] W. A. Benjamin 1967 IX, 246 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fonctions d'une variable complexe Fonctions d'une variable complexe ram Functions of complex variables Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002518286&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Veech, William A. A second course in complex analysis Fonctions d'une variable complexe Fonctions d'une variable complexe ram Functions of complex variables Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4018935-1 |
| title | A second course in complex analysis |
| title_auth | A second course in complex analysis |
| title_exact_search | A second course in complex analysis |
| title_full | A second course in complex analysis William A. Veech, University of California, Berkeley |
| title_fullStr | A second course in complex analysis William A. Veech, University of California, Berkeley |
| title_full_unstemmed | A second course in complex analysis William A. Veech, University of California, Berkeley |
| title_short | A second course in complex analysis |
| title_sort | a second course in complex analysis |
| topic | Fonctions d'une variable complexe Fonctions d'une variable complexe ram Functions of complex variables Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Fonctions d'une variable complexe Functions of complex variables Funktionentheorie |
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