An introduction to abstract harmonic analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Toronto [u.a.]
van Nostrand
1953
|
| Series: | The university series in higher mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 190 S. |
Staff View
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| 245 | 1 | 0 | |a An introduction to abstract harmonic analysis |c by Lynn H. Loomis |
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Record in the Search Index
| _version_ | 1804120455288717312 |
|---|---|
| adam_text | CONTENTS
CHAPTER I: TOPOLOGY
SECTION PAGE
1. Sets 1
2. Topology 3
3. Separation axioms and theorems 5
4. The Stone Weierstrass theorem 8
5. Cartesian products and weak topology 10
CHAPTER II: BANACH SPACES
6. Normed linear spaces 13
7. Bounded linear transformations 15
8. Linear functionals 18
9. The weak topology for X* 22
10. Hilbert space 23
11. Involution on (R(H) 27
CHAPTER III: INTEGRATION
12. The Daniell integral 29
13. Equivalence and measurability 34
14. The real Lp spaces 37
15. The conjugate space of U 40
16. Integration on locally compact Hausdorff spaces 43
17. The complex // spaces 46
CHAPTER IV: BANACH ALGEBRAS
18. Definition and examples 48
19. Function algebras 50
20. Maximal ideals 58
21. Spectrum; adverse 63
22. Banach algebras; elementary theory 66
23. The maximal ideal space of a commutative Banach algebra . 69
24. Some basic general theorems 75
ix
X CONTENTS
CHAPTER V: SOME SPECIAL BANACH ALGEBRAS
SECTION PAGE
25. Regular commutative Banach algebras 82
26. Banach algebras with involutions 87
27. #* algebras 100
CHAPTER VI: THE HAAR INTEGRAL
28. The topology of locally compact groups 108
29. The Haar integral 112
30. The modular function 117
31. The group algebra 120
32. Representations 127
33. Quotient measures 130
CHAPTER VII: LOCALLY COMPACT ABELIAN GROUPS
34. The character group 134
35. Examples 138
36. The Bochner and Plancherel theorems 141
37. Miscellaneous theorems 147
38. Compact Abelian groups and generalized Fourier series . . . 153
CHAPTER VIII: COMPACT GROUPS AND ALMOST PERIODIC FUNCTIONS
39. The group algebra of a compact group 156
40. Representation theory 161
41. Almost periodic functions 165
CHAPTER IX: SOME FURTHER DEVELOPMENTS
42. Non commutative theory 174
43. Commutative theory 179
Bibliography 185
Index 188
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:42:21Z |
| institution | BVB |
| language | English |
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| physical | X, 190 S. |
| publishDate | 1953 |
| publishDateSearch | 1953 |
| publishDateSort | 1953 |
| publisher | van Nostrand |
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| series2 | The university series in higher mathematics |
| spelling | Loomis, Lynn H. 1915-1994 Verfasser (DE-588)172230314 aut An introduction to abstract harmonic analysis by Lynn H. Loomis Toronto [u.a.] van Nostrand 1953 X, 190 S. txt rdacontent n rdamedia nc rdacarrier The university series in higher mathematics Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003940614&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Loomis, Lynn H. 1915-1994 An introduction to abstract harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4023453-8 |
| title | An introduction to abstract harmonic analysis |
| title_auth | An introduction to abstract harmonic analysis |
| title_exact_search | An introduction to abstract harmonic analysis |
| title_full | An introduction to abstract harmonic analysis by Lynn H. Loomis |
| title_fullStr | An introduction to abstract harmonic analysis by Lynn H. Loomis |
| title_full_unstemmed | An introduction to abstract harmonic analysis by Lynn H. Loomis |
| title_short | An introduction to abstract harmonic analysis |
| title_sort | an introduction to abstract harmonic analysis |
| topic | Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Harmonische Analyse |
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