A primer of real analytic functions:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Boston [u.a.]
Birkhäuser
2002
|
| Edition: | 2. ed. |
| Series: | Birkhäuser advanced texts
Basler Lehrbücher |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 205 S. graph. Darst. |
| ISBN: | 3764342641 0817642641 |
Staff View
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| 245 | 1 | 0 | |a A primer of real analytic functions |c Steven G. Krantz ; Harold R. Parks |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2002 | |
| 300 | |a XII, 205 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804129405699620864 |
|---|---|
| adam_text | Contents
Preface to the Second Edition ix
Preface to the First Edition xi
1 Elementary Properties 1
1.1 Basic Properties of Power Series 1
1.2 Analytic Continuation 11
1.3 The Formula of Faa di Bruno 16
1.4 Composition of Real Analytic Functions 18
1.5 Inverse Functions 20
2 Multivariable Calculus of Real Analytic Functions 25
2.1 Power Series in Several Variables 25
2.2 Real Analytic Functions of Several Variables 29
2.3 The Implicit Function Theorem 35
2.4 A Special Case of the Cauchy Kowalewsky Theorem 42
2.5 The Inverse Function Theorem 47
2.6 Topologies on the Space of Real Analytic Functions 50
2.7 Real Analytic Submanifolds 54
2.7.1 Bundles over a Real Analytic Submanifold 56
2.8 The General Cauchy Kowalewsky Theorem 61
viii Contents
3 Classical Topics 67
3.0 Introductory Remarks 67
3.1 The Theorem of Pringsheim and Boas 68
3.2 Besicovitch s Theorem 72
3.3 Whitney s Extension and Approximation Theorems 75
3.4 The Theorem of S.Bernstein 79
4 Some Questions of Hard Analysis 83
4.1 Quasi analytic and Gevrey Classes 83
4.2 Puiseux Series 95
4.3 Separate Real Analyticity 104
5 Results Motivated by Partial Differential Equations 115
5.1 Division of Distributions I 115
5.1.1 Projection of Polynomially Defined Sets 117
5.2 Division of Distributions II 126
5.3 The FBI Transform 135
5.4 The Paley Wiener Theorem 144
6 Topics in Geometry 151
6.1 The Weierstrass Preparation Theorem 151
6.2 Resolution of Singularities 156
6.3 Lojasiewicz s Structure Theorem for Real Analytic Varieties . . .166
6.4 The Embedding of Real Analytic Manifolds 171
6.5 Semianalytic and Subanalytic Sets 177
6.5.1 Basic Definitions 177
6.5.2 Facts Concerning Semianalytic and Subanalytic Sets . . . 179
6.5.3 Examples and Discussion 181
6.5.4 Rectilinearization 184
Bibliography 187
Index 203
|
| any_adam_object | 1 |
| author | Krantz, Steven G. 1951- Parks, Harold R. |
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| author_facet | Krantz, Steven G. 1951- Parks, Harold R. |
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| author_sort | Krantz, Steven G. 1951- |
| author_variant | s g k sg sgk h r p hr hrp |
| building | Verbundindex |
| bvnumber | BV014641001 |
| callnumber-first | Q - Science |
| callnumber-label | QA331 |
| callnumber-raw | QA331.5 |
| callnumber-search | QA331.5 |
| callnumber-sort | QA 3331.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 420 |
| ctrlnum | (OCoLC)49512682 (DE-599)BVBBV014641001 |
| dewey-full | 515/.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.8 |
| dewey-search | 515/.8 |
| dewey-sort | 3515 18 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV014641001 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:04:37Z |
| institution | BVB |
| isbn | 3764342641 0817642641 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009942891 |
| oclc_num | 49512682 |
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| physical | XII, 205 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Birkhäuser advanced texts Basler Lehrbücher |
| spelling | Krantz, Steven G. 1951- Verfasser (DE-588)130535907 aut A primer of real analytic functions Steven G. Krantz ; Harold R. Parks 2. ed. Boston [u.a.] Birkhäuser 2002 XII, 205 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Birkhäuser advanced texts Basler Lehrbücher Analyse mathématique Fonctions analytiques ram Fonctions de variables réelles Functions of real variables Mathematical analysis Reelle Funktion (DE-588)4048918-8 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 s DE-604 Reelle Funktion (DE-588)4048918-8 s Parks, Harold R. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009942891&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krantz, Steven G. 1951- Parks, Harold R. A primer of real analytic functions Analyse mathématique Fonctions analytiques ram Fonctions de variables réelles Functions of real variables Mathematical analysis Reelle Funktion (DE-588)4048918-8 gnd Analytische Funktion (DE-588)4142348-3 gnd |
| subject_GND | (DE-588)4048918-8 (DE-588)4142348-3 |
| title | A primer of real analytic functions |
| title_auth | A primer of real analytic functions |
| title_exact_search | A primer of real analytic functions |
| title_full | A primer of real analytic functions Steven G. Krantz ; Harold R. Parks |
| title_fullStr | A primer of real analytic functions Steven G. Krantz ; Harold R. Parks |
| title_full_unstemmed | A primer of real analytic functions Steven G. Krantz ; Harold R. Parks |
| title_short | A primer of real analytic functions |
| title_sort | a primer of real analytic functions |
| topic | Analyse mathématique Fonctions analytiques ram Fonctions de variables réelles Functions of real variables Mathematical analysis Reelle Funktion (DE-588)4048918-8 gnd Analytische Funktion (DE-588)4142348-3 gnd |
| topic_facet | Analyse mathématique Fonctions analytiques Fonctions de variables réelles Functions of real variables Mathematical analysis Reelle Funktion Analytische Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009942891&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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