Proceedings of the Symposium on Complex Analysis Canterbury 1973 (London Mathematical Society Lecture Note Series, Series Number 12)

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. Cover......Page 1 Title Page......Page 2 Copyright Page......Page 3 Contents......Page 4 A minimal-area problem in conformal mapping......Page 10 A remark on schlicht functions with quasiconformal extensions......Page 16 Some extremal problems for univalent functions, harmonic measures, and subharmonic functions......Page 20 On coefficient problems for certain power series......Page 26 Approximation by analytic functions uniformly continuous on a set......Page 38 A meromorphic function with assigned Nevanlinna deficiencies......Page 40 Estimation of coefficients of univalent functions by Tauberian remainder theorems......Page 52 The Pade table of functions having a finite number of essential singularities......Page 54 Extremal problems of the cos 7rp-type......Page 58 A cos TrA-problem and a differential inequality......Page 62 Applications of Denjoy integral inequalities to growth problems for subharmonic and meromorphic functions......Page 68 A theorem on mini z i log|f(z) | /T( r , f)......Page 78 The L^-integrability of the partial derivatives of a quasiconformal mapping......Page 82 A Hilbert space method in the theory of schlicht functions......Page 84 An extremal problem concerning entire functions with radially distributed zeros......Page 90 Local behavior of subharmonic functions......Page 98 A general form of the annulus theorem......Page 100 Two problems on H^P spaces......Page 102 Approximation on curves by linear combinations of exponentials......Page 106 Two results on means of harmonic functions......Page 110 The Fatou limits of outer functions......Page 114 A proof of I a | ^ 4 by Loewner's method......Page 116 Completeness questions and related Dirichlet polynomials......Page 120 On the boundary behaviour of normal functions......Page 122 Joint approximation in the complex domain......Page 124 Some linear operators in function theory......Page 128 Analogues of the elliptic modular functions in R^3......Page 134 On some phenomena and problems of the powersum-method......Page 138 Meromorphic functions with large sums of deficiencies......Page 142 On D. J. PatilTs remarkable generalisation of Cauchy's formula......Page 146 Analytic functions and harmonic analysis......Page 148 Progress on the previous problems......Page 152 New problems......Page 164