Sampling, Approximation, and Signal Analysis: Harmonic Analysis in the Spirit of J. Rowland Higgins (Applied and Numerical Harmonic Analysis)

During his long and distinguished career, J. Rowland Higgins (1935-2020) made a substantial impact on many mathematical fields through his work on sampling theory, his deep knowledge of its history, and his service to the community.  This volume is a tribute to his work and legacy, featuring chapters written by distinguished mathematicians that explore cutting-edge research in sampling, approximation, signal analysis, and other related areas.  An introductory chapter provides a biography of Higgins that explores his rich and unique life, along with a bibliography of his papers; a brief history of the SampTA meetings – of which he was a Founding Member – is also included.  The remaining articles are grouped into four sections – classical sampling, theoretical extensions, frame theory, and applications of sampling theory – and explore Higgins’ contributions to these areas, as well as some of the latest developments.

​Maurice Dodson is a Professor Emeritus of Mathematics at the University of York. He wrote over seventy papers, co-authored 1 book and co-edited another. His interests broadened to Diophantine approximation and the metrical theory and further to dynamical systems and their many applications, including the WKS sampling theorem and its variety of applications, the last stemming from a connection with X-ray  crystallography. This led to meeting Rowland Higgins in 1985 and the start of a long productive collaboration, often with a number of authors, in sampling theory and its applications and extensions, particularly to LCA groups and Kluvanek’s theorem and to sampling for function spaces.