1 Meromorphic Functions.- 2 Entire Functions.- 3 Subharmonic and Harmonic Functions.- 4 Polynomials.-5 Functions in the Unit Disk.- 6 Univalent and Multivalent Functions.- 7 Miscellaneous.- 8 Spaces of Functions.- 9 Interpolation and Approximation
Walter K. Hayman is an Emeritus Professor at Imperial College London. The author of five influential books, he is best known for his fundamental work on the theory of functions. Over the course of his career, he has made many outstanding contributions to the study of functions of a complex variable, notably providing solutions to some of the most famous problems in the field. Foremost amongst these is the so-called asymptotic Bieberbach conjecture, for which he provided a definitive proof in 1955. With Margaret Hayman, he founded the British Mathematical Olympiad. He was elected to the Royal Society in 1956, earlier than any other living member bar one (Freeman Dyson). The author of over 200 scientific papers, Walter has won many of the most prestigious accolades in his field and has received honorary degrees from universities in four countries. Eleanor F. Lingham is a Senior Lecturer at Sheffield Hallam University. She studied for her undergraduate and Masters degrees at University College Cork, and for her PhD at the University of Nottingham.
"It is an absorbing, indeed addictive, volume for anyone interested in complex variables. ... I encourage every reader of this review to get a copy of this wonderful book." (Christopher Bishop, Mathematical Reviews, June, 2020)