Early life
He was born in the coal-mining village of Newstead, Nottinghamshire, the only child of mineworker and former coalminer William Henstock and Mary Ellen Henstock (née Bancroft). On the Henstock side he was descended from 17th century Flemish people, Flemish immigrants called Hemstok. Because of his early academic promise it was expected that Henstock would attend the University of Nottingham where his father and uncle had received technical education, but as it turned out he won scholarships which enabled him to study mathematics at St John's College, Cambridge from October 1941 until November 1943, when he was sent for war service to the Ministry of Supply's department of Statistical Method and Quality Control in London. This work did not satisfy him, so he enrolled at Birkbeck, University of London, Birkbeck College, London where he joined the weekly seminar of Professor Paul Dienes which was then a focus for mathematical activity in London. Henstock wanted to study divergent series but Dienes prevailed upon him to get involved in the theory of Integral, integration, thereby setting him on course for his life's work. A devoted Methodist, the lasting impression he made was one of gentle sincerity and amiability. Henstock married Marjorie Jardine in 1949. Their son John was born 10 July 1952. Ralph Henstock died on 17 January 2007 after a short illness.Work
He was awarded the University of Cambridge#Mathematics and mathematical physics, Cambridge B.A. in 1944 and began research for the PhD#United Kingdom, PhD in Birkbeck College, London, under the supervision of Paul Dienes. His PhD thesis, entitledList of publications of Ralph Henstock
Much of Henstock's earliest work was published by the List of scientific journals in mathematics, Journal of the London Mathematical Society. These were "On interval functions and their integrals" I (21, 1946) and II (23, 1948); "The efficiency of matrices for Taylor series" (22, 1947); "The efficiency of matrices for bounded sequences" (25, 1950); "The efficiency of convergence factors for functions of a continuous real variable" (30, 1955); "A new description of the Ward integral" (35 1960); and "The integrability of functions of interval functions" (39 1964). His works, published in ''Proceedings of the London Mathematical Society'', were "Density integration" (53, 1951); "On the measure of sum sets (I) The theorems of Brunn, Minkowski, and Lusternik, (with A.M. McBeath)" ([3] 3, 1953); "Linear functions with domain a real countably infinite dimensional space" ([3] 5, 1955); "Linear and bilinear functions with domain contained in a real countably infinite dimensional space" ([3] 6, 1956); "The use of convergence factors in Ward integration" ([3] 10, 1960); "The equivalence of generalized forms of the Ward, variational, Denjoy-Stieltjes, and Perron-Stieltjes integrals" ([3] 10, 1960); "N-variation and N-variational integrals of set functions" ([3] 11, 1961); "Definitions of Riemann type of the variational integrals" ([3] 11, 1961); "Difference-sets and the Banach–Steinhaus theorem" ([3] 13, 1963); "Generalized integrals of vector-valued functions ([3] 19 1969) His additional papers were #Sets of uniqueness for trigonometric series and integrals, Proceedings of the Cambridge Philosophical Society 46 (1950) 538–548. #On Ward's Perron-Stieltjes integral, Canadian Journal of Mathematics 9 (1957) 96–109. #The summation by convergence factors of Laplace-Stieltjes transform, Laplace-Stieltjes integrals outside their half plane of convergence, Mathematische Zeitschrift 67 (1957) 10–31. #Theory of Integration, Butterworths, London, 1962. #Tauberian theorems for integrals, Canadian Journal of Mathematics 15 (1963) 433–439. #Majorants in variational integration, Canadian Journal of Mathematics 18 (1966) 49–74. #A Riemann-type integral of Lebesgue power, Canadian Journal of Mathematics 20 (1968) 79–87. #Linear Analysis, Butterworths, London, 1968. #Integration by parts, Aequationes Mathematicae 9 (1973) 1–18. #The N-variational integral and the Schwartz distributions III, Journal of the London Mathematical Society (2) 6 (1973) 693–700. #Integration in product spaces, including Wiener and Feynman integration, Proceedings of the London Mathematical Society (3) 27 (1973) 317–344. #Additivity and the Lebesgue limit theorems, The Greek Mathematical Society C. Carathéodory Symposium, 1973, 223–241 (Proceedings published 1974).Review of Henstock's work
The journal Scientiae Mathematicae Japonicae published a special commemorative issue in his honor, January 2008. The above article is copied, with permission, from Real Analysis Exchange and from Scientiae Mathematicae Japonicae. The latter contains the following review of Henstock's work: 1. Ralph Henstock, an obituary, by P. Bullen. 2. Ralph Henstock: research summary, by E. Talvila. 3. The integral à la Henstock, by Peng Yee Lee. 4. The natural integral on the real line, by B. Thomson. 5. Ralph Henstock's influence on integration theory, by W.F. Pfeffer. 6. Henstock on random variation, by P. Muldowney. 7. Henstock integral in harmonic analysis, by V.A. Skvortsov. 8. Convergences on the Henstock-Kurzweil integral, by S. Nakanishi.See also
*Partition of an interval *Integrable functionReferences
* * * Whole Number 247 * {{DEFAULTSORT:Henstock, Ralph 1923 births 2007 deaths 20th-century English mathematicians 21st-century English mathematicians Mathematical analysts Academics of Queen's University Belfast Academics of the University of Bristol Academics of Lancaster University Academics of Ulster University Alumni of Birkbeck, University of London Alumni of St John's College, Cambridge English Methodists