Synopses & Reviews
An international conference on complex analysis was held in Canterbury in July 1973. Some of the world's most prominent complex analysts attended and some outstanding open problems had their first solutions announced there. These are reflected in this set of Proceedings. Almost all of the contributions are abstracts of talks given at the symposium. The final part of this volume is a section on research problems contributed by members of the conference and a report on a previous collection of problems edited by Professor W. K. Hayman after an earlier conference in 1964. This book is essential reading for research workers and graduate students interested in complex analysis.
Synopsis
This book is essential reading for research workers and graduate students interested in complex analysis.
Table of Contents
Part I. Contributions of participants: 1. A minimal-area problem in conformal mapping Dov Aharonov and Harold S. Shapiro; 2. A remark on schlicht functions with quasi-conformal extensions Lars V. Ahlfors; 3. Some extremal problems for univalent functions, harmonic measures, and subharmonic functions Albert Baernstein; 4. On coefficient problems for certain power series D. A. Brannan; 5. Approximation by analytic functions uniformly continuous on a set Leon Brown and Allen Shields; 6. A meromorphic function with assigned Nevanlinna deficiencies David Drasin; 7. Estimation of coefficients of univalent functions by Tauberian remainder theorems Peter L. Duren; 8. The Pade table of functions having a finite number of essential singularities Albert Edrei; 9. Extremal problems of the cos-type Albert Edrei; 10. A cos-problem and a differential inequality Matts Essen; 11. Applications of Denjoy integral inequalities to growth problems for subharmonic and meromorphic functions Matts Essen and Daniel F. Shea; 12. A theorem on min I z I log I f (z) I /T(r, f) W. H. J. Fuchs; 13. The LP- integrability of the partial derivatives of a quasi-conformal mapping F. W. Gehring; 14. A Hilbert space method in the theory of schlicht functions H. Grunsky and James A. Jenkins; 15. An extremal problem concerning entire functions with radially distributed zeros Simon Hellerstein and Daniel F. Shea; 16. Local behavior of subharmonic functions A. Huber; 17. A general form of the annulus theorem James A. Jenkins; 18. Two problems on HP spaces J. P. Kahane; 19. Approximation on curves by linear combinations of exponentials J. Korevaar; 20. Two results on means of harmonic functions U. Kuran; 21. The Fatou limits of outer functions A. J. Lohwater and G. Piranian; 22. A proof Zeev Nehari; 23. Completeness questions and related Dirichlet polynomials D. J. Newman; 24. On the boundary behaviour of normal functions Ch. Pommerenke; 25. Joint approximation in the complex domain L. A. Rubel; 26. Some linear operators in function theory T. B. Sheil-Small; 27. Analogues of the elliptic modular functions in R3 Uri Srebrt; 28. On some phenomena and problems of the powersum- method Paul Turan; 29. Meromorphic functions with large sums of deficiencies Allen Weitsman; 30. On D. J. Patil's remarkable generalisation of Cauchy's formula L. C. Young; 31. Analytic functions and harmonic analysis Lawrence Zalcman; Part II. Research problems in function theory: W. K. Hayman; Progress on the previous problems; New problems.