Research Catalog

Title

The Cauchy transform, potential theory, and conformal mapping / Steven R. Bell.

Author

Bell, Steven Robert.

Publication

Boca Raton, Fl. : CRC Press, ©1992.

Items in the Library & Off-site

Details

Description

x, 149 pages : illustrations; 25 cm.

Series Statement

Studies in advanced mathematics

Uniform Title

Studies in advanced mathematics

Subject

• Cauchy transform
• Functions of complex variables
• Potential theory (Mathematics)
• Conformal mapping
• Cauchy, Transformée de
• Fonctions d'une variable complexe
• Théorie du potentiel
• Applications conformes
• Functies (wiskunde)
• Complexe variabelen
• Funcoes (matematica)
• Potentiel, théorie de
• Fonctions de plusieurs variables complexes
• Cauchy, problèmes de
• Représentation des surfaces
• Potentiel, Théorie du
• Transformations (mathématiques)
• Équations différentielles

Bibliography (note)

• Includes bibliographical references (p. 141-143) and index.

Contents

1. Introduction -- 2. The improved Cauchy Integral formula -- 3. The Cauchy transform -- 4. The Hardy space, the Szego projection, and the Kerzman-Stein formula -- 5. The Kerzman-Stein operator and kernel -- 6. The classical definition of the Hardy space -- 7. The Szego kernel function -- 8. The Riemann mapping function -- 9. A density lemma and consequences -- 10. Solution of the Dirichlet Problem in simply connected domains -- 11. The case of real analytic boundary -- 12. The transformation law for the Szego kernel under conformal mappings -- 13. The Ahlfors map of a multiply connected domain -- 14. The Dirichlet problem in multiply connected domains -- 15. The Bergman space -- 16. Proper holomorphic mappings and the Bergman projection -- 17. The solid Cauchy transform -- 18. The classical Neumann problem -- 19. Harmonic measure and the Szego kernel -- 20. The Neumann problem in multiply connected domains -- 21. The Dirichlet problem again -- 22. The Hilbert transform -- 23. The Bergman kernel and the Szego kernel -- 24. Pseudolocal property of the Cauchy transform and consequences -- 25. Zeroes of the Szego kernel -- 26. The Kerzman-Stein integral equation -- 27. Local boundary behavior of holomorphic mappings -- 28. The dual space of A [superscript Infinity] [Omega] -- 29. The Green's function and the Bergman kernel -- 30. Zeroes of the Bergman kernel -- Appendix A. The Cauchy-Kovalevski Theorem for the Cauchy-Riemann operator.

ISBN

• 084938270X
• 9780849382703

LCCN

92013066

OCLC

• ocm25746633
• 25746633
• SCSB-1956743

Owning Institutions

Princeton University Library