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Bosanquet's early 1930's papers were on series and integration, a 1930 paper being on fractional integration, a topic he would return to many times.
His first and only appointment was to the University of London. He was appointed in 1929 as a Lecturer, becoming a Reader in 1936 and finally a Professor in 1966. He retired in 1971 and some time later moved from London to Cambridge. He spent a few periods away from London. For example he was a visiting professor at the University of Utah during 1964-65 a gave a major lecture series on The history and development of the theory of divergent series and integrals. During 1969-70 he visited the University of Western Ontario and gave a major lecture series on Matrix transformations and sequence spaces with applications to summability.
Bosanquet wrote many papers on the convergence and summability of Fourier series. He also wrote on the convergence and summability of Dirichlet series and studied specific kinds of summability such as summability factors for Cesàro means. His later work on integrals include two major papers on the Laplace-Stieltjes integral published in 1953 and 1961. Other topics he studied included inequalities, mean-value theorems, Tauberian theorems and convexity theorems.
Over a period of 30 years, Bosanquet supervised 19 students for their doctorate. He had a reputation for being a excellent supervisor who was always ready to offer help and advice to his students but still encouraged them to find directions of their own. C A Rogers, one of his students, writes in [1] :-
He was an extremely generous mathematician, always striving to help and encourage his students to sharpen their ideas.In [2] Russell talks about Bosanquet's writing and lecturing skills saying:-
But if his papers show a meticulous observance to accuracy down to the last comma, he often cast caution aside in his letters and his lectures, and one could obtain from these the flavour of heuristic which showed his mind at work. He drew his audience along with him, inviting them to contradict him or suggest a different direction.
Article by: J J O'Connor and E F Robertson
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JOC/EFR December 1996
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