An introduction to multicomplex spaces and functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
1991
|
| Schriftenreihe: | Pure and applied mathematics
140 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 402 S. |
| ISBN: | 082478345X |
Internformat
MARC
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| 650 | 7 | |a dérivée |2 inriac | |
| 650 | 7 | |a fonction complexe |2 inriac | |
| 650 | 7 | |a fonction holomorphe |2 inriac | |
| 650 | 7 | |a intégrale |2 inriac | |
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Datensatz im Suchindex
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| adam_text | Contents
FOREWORD Olga Taussky Todd iii
PREFACE v
Chapter 1. THE BICOMPLEX SPACE 1
1. Introduction 1
2. C2: A Linear Space 3
3. C2: A Banach Space 4
4. Multiplication 6
5. Fractions and Quotients 13
6. The Idempotent Representation 18
7. Two Principal Ideals 25
8. The Auxiliary Complex Spaces 34
9. The Discus 44
Chapter 2. FUNCTIONS DEFINED BY BICOMPLEX
POWER SERIES 53
10. Introduction 53
11. Limits of Sequences 55
12. Infinite Series 57
xi
xii Contents
13. Power Series 61
14. Functions Represented by Power Series 72
15. Holomorphic Functions of a Bicomplex Variable 83
16. Algebras of Holomorphic Functions 94
17. Elementary Functions 104
18. The Logarithm Function 122
Chapter 3. DERIVATIVES AND HOLOMORPHIC
FUNCTIONS 131
19. Introduction 131
20. Derivatives and the Stolz Condition 134
21. Differentiability Implies the Strong Stolz Condition 143
22. The Weak Stolz Condition Implies Differentiability 148
23. Differentiability: Necessary Conditions 155
24. Differentiability: Sufficient Conditions 164
25. Holomorphic and Differentiate Functions 175
26. The Calculus of Derivatives 179
27. The Taylor Series of a Holomorphic Function 184
28. Isomorphic Bicomplex Algebras and Cauchy Riemann
Matrices 187
29. Holomorphic Functions and Their Inverses 194
Chapter 4. INTEGRALS AND HOLOMORPHIC
FUNCTIONS 202
30. Introduction 202
31. Curves in C2 204
32. Integrals of Functions with Values in C2 210
33. The Fundamental Theorem of the Integral Calculus 222
34. Cauchy s Integral Theorem: A Special Case 235
35. Existence of Primitives 240
36. Cauchy s Integral Theorem: The General Case 244
37. Integrals Independent of the Path 248
38. Integrals and the Idempotent Representation 255
39. Cauchy s Integral Theorem and the Idempotent
Representation 263
40. Cauchy s Integral Formula 276
41. Taylor Series 291
42. Sequences of Holomorphic Functions 301
Contents xiii
Chapter 5. GENERALIZATIONS TO HIGHER
DIMENSIONS 306
43. Introduction 306
44. The Spaces CB 307
45. The Idempotent Representation 313
46. Singular Elements; Cauchy Riemann Matrices 322
47. Power Series and Holomorphic Functions in Cn 343
48. Derivatives of Functions in Cn 354
49. Integrals and Their Applications 373
Chapter 6. EPILOGUE 395
BIBLIOGRAPHY 397
INDEX 399
|
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| id | DE-604.BV004413898 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:12:43Z |
| institution | BVB |
| isbn | 082478345X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002738488 |
| oclc_num | 21975150 |
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| owner | DE-12 DE-384 DE-739 DE-703 DE-11 |
| owner_facet | DE-12 DE-384 DE-739 DE-703 DE-11 |
| physical | XIII, 402 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Price, Griffith Baley Verfasser aut An introduction to multicomplex spaces and functions G. Baley Price New York [u.a.] Dekker 1991 XIII, 402 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 140 Banach, algèbres de ram Fonctions holomorphes ram algèbre Banach inriac dérivée inriac fonction complexe inriac fonction holomorphe inriac intégrale inriac Banach algebras Holomorphic functions Banach-Algebra (DE-588)4193187-7 gnd rswk-swf Holomorphe Funktion (DE-588)4025645-5 gnd rswk-swf Banach-Algebra (DE-588)4193187-7 s Holomorphe Funktion (DE-588)4025645-5 s DE-604 Pure and applied mathematics 140 (DE-604)BV000001885 140 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002738488&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Price, Griffith Baley An introduction to multicomplex spaces and functions Pure and applied mathematics Banach, algèbres de ram Fonctions holomorphes ram algèbre Banach inriac dérivée inriac fonction complexe inriac fonction holomorphe inriac intégrale inriac Banach algebras Holomorphic functions Banach-Algebra (DE-588)4193187-7 gnd Holomorphe Funktion (DE-588)4025645-5 gnd |
| subject_GND | (DE-588)4193187-7 (DE-588)4025645-5 |
| title | An introduction to multicomplex spaces and functions |
| title_auth | An introduction to multicomplex spaces and functions |
| title_exact_search | An introduction to multicomplex spaces and functions |
| title_full | An introduction to multicomplex spaces and functions G. Baley Price |
| title_fullStr | An introduction to multicomplex spaces and functions G. Baley Price |
| title_full_unstemmed | An introduction to multicomplex spaces and functions G. Baley Price |
| title_short | An introduction to multicomplex spaces and functions |
| title_sort | an introduction to multicomplex spaces and functions |
| topic | Banach, algèbres de ram Fonctions holomorphes ram algèbre Banach inriac dérivée inriac fonction complexe inriac fonction holomorphe inriac intégrale inriac Banach algebras Holomorphic functions Banach-Algebra (DE-588)4193187-7 gnd Holomorphe Funktion (DE-588)4025645-5 gnd |
| topic_facet | Banach, algèbres de Fonctions holomorphes algèbre Banach dérivée fonction complexe fonction holomorphe intégrale Banach algebras Holomorphic functions Banach-Algebra Holomorphe Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002738488&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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