Holdings: Complex analysis :: THWS Bibkatalog

Complex analysis:

Saved in:

Bibliographic Details
Main Author:	Lang, Serge 1927-2005 (Author)
Format:	Book
Language:	English
Published:	New York u.a. Springer 1993
Edition:	3. ed.
Series:	Graduate texts in mathematics 103
Subjects:	Analyse mathématique Fonctions d'une variable complexe Functions of complex variables Mathematical analysis Funktionalanalysis Funktionentheorie Einführung
Online Access:	Inhaltsverzeichnis
Physical Description:	XIV, 458 S. graph. Darst.
ISBN:	0387978860 3540978860

Staff View

MARC


LEADER	00000nam a2200000 cb4500
001	BV006159144
003	DE-604
005	00000000000000.0
007	t
008	930204s1993 d\|\|\| \|\|\|\| 00\|\|\| eng d
020			\|a 0387978860 \|9 0-387-97886-0
020			\|a 3540978860 \|9 3-540-97886-0
035			\|a (OCoLC)26013113
035			\|a (DE-599)BVBBV006159144
040			\|a DE-604 \|b ger \|e rakddb
041	0		\|a eng
049			\|a DE-384 \|a DE-824 \|a DE-858 \|a DE-91G \|a DE-11 \|a DE-188
050		0	\|a QA331.7
082	0		\|a 515/.9 \|2 20
084			\|a SK 700 \|0 (DE-625)143253: \|2 rvk
084			\|a MAT 300f \|2 stub
100	1		\|a Lang, Serge \|d 1927-2005 \|e Verfasser \|0 (DE-588)119305119 \|4 aut
245	1	0	\|a Complex analysis \|c Serge Lang
250			\|a 3. ed.
264		1	\|a New York u.a. \|b Springer \|c 1993
300			\|a XIV, 458 S. \|b graph. Darst.
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
490	1		\|a Graduate texts in mathematics \|v 103
650		4	\|a Analyse mathématique
650		7	\|a Analyse mathématique \|2 ram
650		4	\|a Fonctions d'une variable complexe
650		7	\|a Fonctions d'une variable complexe \|2 ram
650		4	\|a Functions of complex variables
650		4	\|a Mathematical analysis
650	0	7	\|a Funktionalanalysis \|0 (DE-588)4018916-8 \|2 gnd \|9 rswk-swf
650	0	7	\|a Funktionentheorie \|0 (DE-588)4018935-1 \|2 gnd \|9 rswk-swf
655		7	\|0 (DE-588)4151278-9 \|a Einführung \|2 gnd-content
689	0	0	\|a Funktionentheorie \|0 (DE-588)4018935-1 \|D s
689	0		\|5 DE-604
689	1	0	\|a Funktionalanalysis \|0 (DE-588)4018916-8 \|D s
689	1		\|8 1\p \|5 DE-604
830		0	\|a Graduate texts in mathematics \|v 103 \|w (DE-604)BV000000067 \|9 103
856	4	2	\|m HBZ Datenaustausch \|q application/pdf \|u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003896413&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA \|3 Inhaltsverzeichnis
999			\|a oai:aleph.bib-bvb.de:BVB01-003896413
883	1		\|8 1\p \|a cgwrk \|d 20201028 \|q DE-101 \|u https://d-nb.info/provenance/plan#cgwrk

Record in the Search Index

_version_	1804120388921196544
adam_text	Contents Foreword v Prerequisites ix PART ONE Basic Theory 1 CHAPTER I Complex Numbers and Functions 3 §1. Definition 3 §2. Polar Form 8 §3. Complex Valued Functions 12 §4. Limits and Compact Sets 17 Compact Sets 21 §5. Complex Differentiability 27 §6. The Cauchy Riemann Equations 31 §7. Angles Under Holomorphic Maps 33 CHAPTER II Power Series 37 §1. Formal Power Series 37 §2. Convergent Power Series 47 §3. Relations Between Formal and Convergent Series 60 Sums and Products 60 Quotients 64 Composition of Series 66 §4. Analytic Functions 68 §5. Differentiation of Power Series 72 xii CONTENTS §6. The Inverse and Open Mapping Theorems 76 §7. The Local Maximum Modulus Principle 83 CHAPTER III Cauchy s Theorem, First Part 86 §1. Holomorphic Functions on Connected Sets 86 Appendix: Connectedness 92 §2. Integrals Over Paths 94 §3. Local Primitive for a Holomorphic Function 104 §4. Another Description of the Integral Along a Path 110 §5. The Homotopy Form of Cauchy s Theorem 116 §6. Existence of Global Primitives. Definition of the Logarithm 119 §7. The Local Cauchy Formula 126 CHAPTER IV Winding Numbers and Cauchy s Theorem 133 §1. The Winding Number 134 §2. The Global Cauchy Theorem 138 Dixon s Proof of Theorem 2.5 (Cauchy s Formula) 147 §3. Artin s Proof 149 CHAPTER V Applications of Cauchy s Integral Formula 156 §1. Uniform Limits of Analytic Functions 156 §2. Laurent Series 161 §3. Isolated Singularities 165 Removable Singularities 165 Poles 166 Essential Singularities 168 CHAPTER VI Calculus of Residues 173 §1. The Residue Formula 173 Residues of Differentials 184 §2. Evaluation of Definite Integrals 191 Fourier Transforms 194 Trigonometric Integrals 197 Mellin Transforms 199 CHAPTER VII Conformal Mappings 208 §1. Schwarz Lemma 210 §2. Analytic Automorphisms of the Disc 212 §3. The Upper Half Plane 215 §4. Other Examples 218 §5. Fractional Linear Transformations 227 CONTENTS xiii CHAPTER VIII Harmonic Functions 237 §1. Definition 237 Application: Perpendicularity 241 Application: Flow Lines 242 §2. Examples 247 §3. Basic Properties of Harmonic Functions 254 §4. The Poisson Formula 264 §5. Construction of Harmonic Functions 267 PART TWO Geometric Function Theory 277 CHAPTER IX Schwarz Reflection 279 §1. Schwarz Reflection (by Complex Conjugation) 279 §2. Reflection Across Analytic Arcs 283 §3. Application of Schwarz Reflection 287 CHAPTER X The Riemann Mapping Theorem 291 §1. Statement of the Theorem 291 §2. Compact Sets in Function Spaces 293 §3. Proof of the Riemann Mapping Theorem 296 §4. Behavior at the Boundary 299 CHAPTER XI Analytic Continuation Along Curves 307 §1. Continuation Along a Curve 307 §2. The Dilogarithm 315 §3. Application to Picard s Theorem 319 PART THREE Various Analytic Topics 321 CHAPTER XII Applications of the Maximum Modulus Principle and Jensen s Formula 323 §1. Jensen s Formula 324 §2. The Picard Borel Theorem 330 §3. Bounds by the Real Part, Borel Caratheodory Theorem 338 §4. The Use of Three Circles and the Effect of Small Derivatives 340 Hermite Interpolation Formula 342 §5. Entire Functions with Rational Values 344 §6. The Phragmen Lindelof and Hadamard Theorems 349 xiv CONTENTS CHAPTER XIII Entire and Meromorphic Functions 356 §1. Infinite Products 356 §2. Weierstrass Products 360 §3. Functions of Finite Order 366 §4. Meromorphic Functions, Mittag Leffler Theorem 371 CHAPTER XIV Elliptic Functions 374 §1. The Liouville Theorems 374 §2. The Weierstrass Function 378 §3. The Addition Theorem 383 §4. The Sigma and Zeta Functions 386 CHAPTER XV The Gamma and Zeta Functions 391 §1. The Differentiation Lemma 392 §2. The Gamma Function 396 Weierstrass Product 396 The Mellin Transform 401 Proof of Stirling s Formula 406 §3. The Lerch Formula 412 §4. Zeta Functions 415 CHAPTER XVI The Prime Number Theorem 422 §1. Basic Analytic Properties of the Zeta Function 423 §2. The Main Lemma and its Application 428 §3. Proof of the Main Lemma 431 Appendix 435 §1. Summation by Parts and Non Absolute Convergence 435 §2. Difference Equations 437 §3. Analytic Differential Equations 441 §4. Fixed Points of a Fractional Linear Transformation 445 §5. Cauchy s Formula for C°° Functions 447 Bibliography 454 Index 455
any_adam_object	1
author	Lang, Serge 1927-2005
author_GND	(DE-588)119305119
author_facet	Lang, Serge 1927-2005
author_role	aut
author_sort	Lang, Serge 1927-2005
author_variant	s l sl
building	Verbundindex
bvnumber	BV006159144
callnumber-first	Q - Science
callnumber-label	QA331
callnumber-raw	QA331.7
callnumber-search	QA331.7
callnumber-sort	QA 3331.7
callnumber-subject	QA - Mathematics
classification_rvk	SK 700
classification_tum	MAT 300f
ctrlnum	(OCoLC)26013113 (DE-599)BVBBV006159144
dewey-full	515/.9
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	515 - Analysis
dewey-raw	515/.9
dewey-search	515/.9
dewey-sort	3515 19
dewey-tens	510 - Mathematics
discipline	Mathematik
edition	3. ed.
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02031nam a2200529 cb4500</leader><controlfield tag="001">BV006159144</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">930204s1993 d\|\|\| \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387978860</subfield><subfield code="9">0-387-97886-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540978860</subfield><subfield code="9">3-540-97886-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)26013113</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV006159144</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-858</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA331.7</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.9</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 700</subfield><subfield code="0">(DE-625)143253:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 300f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lang, Serge</subfield><subfield code="d">1927-2005</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)119305119</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Complex analysis</subfield><subfield code="c">Serge Lang</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">3. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York u.a.</subfield><subfield code="b">Springer</subfield><subfield code="c">1993</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIV, 458 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">103</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analyse mathématique</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Analyse mathématique</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fonctions d'une variable complexe</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Fonctions d'une variable complexe</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functions of complex variables</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical analysis</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Funktionentheorie</subfield><subfield code="0">(DE-588)4018935-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4151278-9</subfield><subfield code="a">Einführung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Funktionentheorie</subfield><subfield code="0">(DE-588)4018935-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">103</subfield><subfield code="w">(DE-604)BV000000067</subfield><subfield code="9">103</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003896413&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-003896413</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection>
genre	(DE-588)4151278-9 Einführung gnd-content
genre_facet	Einführung
id	DE-604.BV006159144
illustrated	Illustrated
indexdate	2024-07-09T16:41:18Z
institution	BVB
isbn	0387978860 3540978860
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-003896413
oclc_num	26013113
open_access_boolean
owner	DE-384 DE-824 DE-858 DE-91G DE-BY-TUM DE-11 DE-188
owner_facet	DE-384 DE-824 DE-858 DE-91G DE-BY-TUM DE-11 DE-188
physical	XIV, 458 S. graph. Darst.
publishDate	1993
publishDateSearch	1993
publishDateSort	1993
publisher	Springer
record_format	marc
series	Graduate texts in mathematics
series2	Graduate texts in mathematics
spelling	Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Complex analysis Serge Lang 3. ed. New York u.a. Springer 1993 XIV, 458 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 103 Analyse mathématique Analyse mathématique ram Fonctions d'une variable complexe Fonctions d'une variable complexe ram Functions of complex variables Mathematical analysis Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Funktionentheorie (DE-588)4018935-1 s DE-604 Funktionalanalysis (DE-588)4018916-8 s 1\p DE-604 Graduate texts in mathematics 103 (DE-604)BV000000067 103 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003896413&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Lang, Serge 1927-2005 Complex analysis Graduate texts in mathematics Analyse mathématique Analyse mathématique ram Fonctions d'une variable complexe Fonctions d'une variable complexe ram Functions of complex variables Mathematical analysis Funktionalanalysis (DE-588)4018916-8 gnd Funktionentheorie (DE-588)4018935-1 gnd
subject_GND	(DE-588)4018916-8 (DE-588)4018935-1 (DE-588)4151278-9
title	Complex analysis
title_auth	Complex analysis
title_exact_search	Complex analysis
title_full	Complex analysis Serge Lang
title_fullStr	Complex analysis Serge Lang
title_full_unstemmed	Complex analysis Serge Lang
title_short	Complex analysis
title_sort	complex analysis
topic	Analyse mathématique Analyse mathématique ram Fonctions d'une variable complexe Fonctions d'une variable complexe ram Functions of complex variables Mathematical analysis Funktionalanalysis (DE-588)4018916-8 gnd Funktionentheorie (DE-588)4018935-1 gnd
topic_facet	Analyse mathématique Fonctions d'une variable complexe Functions of complex variables Mathematical analysis Funktionalanalysis Funktionentheorie Einführung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003896413&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000067
work_keys_str_mv	AT langserge complexanalysis

Holdings

There is no print copy available.

Interlibrary loan Place Request Caution: Not in THWS collection! Indexes

MARC

Record in the Search Index

There is no print copy available.

Similar Items