2008, English, Book, Illustrated edition: A second course in complex analysis / William A. Veech. Veech, William A.

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A second course in complex analysis / William A. Veech
 
Bookmark: http://trove.nla.gov.au/version/6417958
Edition
  • Dover edition.
Physical Description
  • 1 online resource (ix, 246 pages) : illustrations.
  • ix, 246 p. : ill. ; 22 cm.
Published
  • Mineola, N.Y. : Dover Publications, 2008.
Language
  • English

Edition details

Title
  • A second course in complex analysis /​ William A. Veech.
Author
  • Veech, William A.
Edition
  • Dover edition.
Published
  • Mineola, N.Y. : Dover Publications, 2008.
Content Types
  • text
Carrier Types
  • online resource
Physical Description
  • 1 online resource (ix, 246 pages) : illustrations.
  • ix, 246 p. : ill. ; 22 cm.
Subjects
Summary
  • A clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. The material is largely classical, with particular emphasis on the geometry of complex mappings. Author William A. Veech, the Edgar Odell Lovett Professor of Mathematics at Rice University, presents the Riemann mapping theorem as a special case of an existence theorem for universal covering surfaces. His focus on the geometry of complex mappings makes frequent use of Schwarz's lemma. He constructs the universal covering surface of an arbitrary planar region and employs the modular function to develop the theorems of Landau, Schottky, Montel, and Picard as consequences of the existence of certain coverings. Concluding chapters explore Hadamard product theorem and prime number theorem.
Contents
  • 6. schwarz's lemma7. non-euclidean geometry; 8. the schwarz reflection principle; chapter 3 the mapping theorems of riemann and koebe; 1. analytic equivalence; 2. local uniform convergence; 3. a theorem of hubwitz; 4. implications of pointwise convergence; 5. implications of convergence on a subset; 6. approximately linear functions-another application of schwarz's lemma; 7. a uniformization theorem; 8. a closer look at the covering; 9. boundary behavior; 10. lindelöf's lemma; 11. facts from topology; 12. continuity at the boundary; 13. a theorem of fejer; chapter 4 the modular function.
  • 1. exceptional values2. the modular configuration; 3. the landau radius; 4. schottky's theorem; 5. normal families; 6. montel's theorem; 7. picard's second theorem; 8. the koebe-faber distortion theorem; 9. bloch's theorem; chapter 5 the hadamard product theorem; 1. infinite pboducts; 2. pboducts of functions; 3. the weierstrass product theorem; 4. functions of finite order; 5. exponent of convergence; 6. canonical products; 7. the borel-carathéodory lemma-another form of schwarz's lemma; 8. a lemma of h. cartan; 9. the hadamard product theorem; 10. the gamma function; 11. standard formulas.
  • Cover; Title; Dedication; Copyright; PREFACE; CONTENTS; CHAPTER 1 ANALYTIC CONTINUATION; 1. THE EXPONENTIAL FUNCTION AND THE LOGARITHM; 2. CONTINUATION SEQUENCES; 3. CONTINUATION ALONG AN ARC; 4. GERMS; 5. EXISTENCE OF CONTINUATIONS; 6. THE WINDING NUMBER; 7. THE ARGUMENT PRINCIPLE; 8. THE MONODROMY THEOREM; 9. COMPOSITION OF GERMS; 10. COMPOSITION OF CONTINUATIONS; 11. COVERING SURFACES; CHAPTER 2 GEOMETRIC CONSIDERATIONS; 1. COMPLEX PROJECTIVE SPACE; 2. LINEAR TRANSFORMATIONS; 3. FRACTIONAL LINEAR TRANSFORMATIONS; 4. PROPERTIES OF FRACTIONAL LINEAR TRANSFORMATIONS; 5. SYMMETRY.
  • 12. THE INTEGRAL REPRESENTATION OF Γ(z)CHAPTER 6 THE PRIME NUMBER THEOREM; 1. DIRICHLET SERIES; 2. NUMBER-THEORETIC FUNCTIONS; 3. STATEMENT OF THE PRIME NUMBER THEOREM; 4. THE RIEMANN ZETA FUNCTION; 5. ANALYTIC CONTINUATION OF ζ(s); 6. RIEMANN'S FUNCTIONAL EQUATION; 7. THE ZEROS OF ζ(s) IN THE CRITICAL STRIP; 8. ζ(s) FOR Re s =​ l; 9. INTEGRAL REPRESENTATION OF DIRICHLET SERIES; 10. INTEGRAL-THEORETIC LEMMAS; 11. WEAK LIMITS; 12. A TAUBERIAN THEOREM; BIBLIOGRAPHY; INDEX.
Notes
  • "An unabridged and slightly corrected republication of the work originally published by W.A. Benjamin, Inc., New York, in 1967."--title page verso.
  • Includes bibliographical references (pages 243-244) and index.
Other Form
  • Print version Veech, William A. Second course in complex analysis. Dover edition 9780486462943
Language
  • English
ISBN
  • 9780486151939 (electronic bk.)
  • 048615193X (electronic bk.)
  • 9780486462943
Dewey Number
  • 515/​.9
Libraries Australia ID
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