The Cauchy Transform, Potential Theory and Conformal Mapping
eBook - PDF

The Cauchy Transform, Potential Theory and Conformal Mapping

  1. 221 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

The Cauchy Transform, Potential Theory and Conformal Mapping

About this book

The Cauchy Transform, Potential Theory and Conformal Mapping explores the most central result in all of classical function theory, the Cauchy integral formula, in a new and novel way based on an advance made by Kerzman and Stein in 1976.The book provides a fast track to understanding the Riemann Mapping Theorem. The Dirichlet and Neumann problems f

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Yes, you can access The Cauchy Transform, Potential Theory and Conformal Mapping by Steven R. Bell in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Chapman and Hall/CRC
Year
2015
Print ISBN
9780367852054
eBook ISBN
9781498727211
Edition
2
Topic
Mathematics
Subtopic
Applied Mathematics
Index
Mathematics

Table of contents

  1. Front Cover
  2. Contents
  3. Preface
  4. Table of symbols
  5. Chapter 1 - Introduction
  6. Chapter 2 - The improved Cauchy integral formula
  7. Chapter 3 - The Cauchy transform
  8. Chapter 4 - The Hardy space, the Szegő projection, and the Kerzman-Stein formula
  9. Chapter 5 - The Kerzman-Stein operator and kernel
  10. Chapter 6 - The classical definition of the Hardy space
  11. Chapter 7 - The Szegő kernel function
  12. Chapter 8 - The Riemann mapping function
  13. Chapter 9 - A density lemma and consequences
  14. Chapter 10 - Solution of the Dirichlet problem in simply connected domains
  15. Chapter 11 - The case of real analytic boundary
  16. Chapter 12 - The transformation law for the Szegő kernel under conformal mappings
  17. Chapter 13 - The Ahlfors map of a multiply connected domain
  18. Chapter 14 - The Dirichlet problem in multiply connected domains
  19. Chapter 15 - The Bergman space
  20. Chapter 16 - Proper holomorphic mappings and the Bergman projection
  21. Chapter 17 - The Solid Cauchy transform
  22. Chapter 18 - The classical Neumann problem
  23. Chapter 19 - Harmonic measure and the Szegő kernel
  24. Chapter 20 - The Neumann problem in multiply connected domains
  25. Chapter 21 - The Dirichlet problem again
  26. Chapter 22 - Area quadrature domains
  27. Chapter 23 - Arc length quadrature domains
  28. Chapter 24 - The Hilbert transform
  29. Chapter 25 - The Bergman kernel and the Szegő kernel
  30. Chapter 26 - Pseudo-local property of the Cauchy transform and consequences
  31. Chapter 27 - Zeroes of the Szegő kernel
  32. Chapter 28 - The Kerzman-Stein integral equation
  33. Chapter 29 - Local boundary behavior of holomorphic mappings
  34. Chapter 30 - The dual space of A∞(Ω)
  35. Chapter 31 - The Green’s function and the Bergman kernel
  36. Chapter 32 - Zeroes of the Bergman kernel
  37. Chapter 33 - Complexity in complex analysis
  38. Chapter 34 - Area quadrature domains and the double
  39. Appendix A - The Cauchy-Kovalevski theorem for the Cauchy-Riemann operator
  40. Bibliographic Notes
  41. Bibliography
  42. Back Cover