Research Problems in Function Theory

In 1967 Walter K. Hayman published 'Research Problems in Function Theory', a list of 141 problems in seven areas of function theory. In the decades following, this list was extended to include two additional areas of complex analysis, updates on progress in solving existing problems, and over 520 research problems from mathematicians worldwide. It became known as 'Hayman's List'. This Fiftieth Anniversary Edition contains the complete 'Hayman's List' for the first time in book form, along with 31 new problems by leading international mathematicians. This list has directed complex analysis research for the last half-century, and the new edition will help guide future research in the subject. The book contains up-to-date information on each problem, gathered from the international mathematics community, and where possible suggests directions for further investigation. Aimed at both early career and established researchers, this book provides the key problems andresults needed to progress in the most important research questions in complex analysis, and documents the developments of the past 50 years.

Provides the complete 'Hayman's List' of over 500 problems for the first time, including 31 new problems Provides research updates on the leading questions in complex analysis Contains over 1,000 references indexed to the associated problems Includes supplementary material: sn.pub/extras

Auteur
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.

Texte du rabat

In 1967 Walter K. Hayman published Research Problems in Function Theory , a list of 141 problems in seven areas of function theory. In the decades following, this list was extended to include two additional areas of complex analysis, updates on progress in solving existing problems, and over 520 research problems from mathematicians worldwide. It became known as Hayman's List . This Fiftieth Anniversary Edition contains the complete Hayman's List for the first time in book form, along with 31 new problems by leading international mathematicians. This list has directed complex analysis research for the last half-century, and the new edition will help guide future research in the subject. The book contains up-to-date information on each problem, gathered from the international mathematics community, and where possible suggests directions for further investigation. Aimed at both early career and established researchers, this book provides the key problems andresults needed to progress in the most important research questions in complex analysis, and documents the developments of the past 50 years.

Résumé

"This book is superbly written, it is a pleasure to read, and it will surely prove to be an indispensable tool for all researchers interested in function theory. ... This up-to-date list of problems will surely keep function theorists intrigued for further 50 years or more." (Risto Korhonen, zbMATH 1455.30002, 2021)

"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)

Contenu
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