Ralph Henstock - Work - List of Publications of Ralph Henstock

List of Publications of Ralph Henstock

Much of Henstock's earliest work was published by the 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, 1953); "Linear functions with domain a real countably infinite dimensional space" ( 5, 1955); "Linear and bilinear functions with domain contained in a real countably infinite dimensional space" ( 6, 1956); "The use of convergence factors in Ward integration" ( 10, 1960); "The equivalence of generalized forms of the Ward, variational, Denjoy-Stieltjes, and Perron-Stieltjes integrals" ( 10, 1960); "N-variation and N-variational integrals of set functions" ( 11, 1961); "Definitions of Riemann type of the variational integrals" ( 11, 1961); "Difference-sets and the Banach–Steinhaus theorem" ( 13, 1963); "Generalized integrals of vector-valued functions ( 19 1969)

His additional papers were

1. Sets of uniqueness for trigonometric series and integrals, Proceedings of the Cambridge Philosophical Society 46 (1950) 538-548.
2. On Ward’s Perron-Stieltjes integral, Canadian Journal of Mathematics 9 (1957) 96-109.
3. The summation by convergence factors of Laplace-Stieltjes integrals outside their half plane of convergence, Mathematische Zeitschrift 67 (1957) 10-31.
4. Theory of Integration, Butterworths, London, 1962.
5. Tauberian theorems for integrals, Canadian Journal of Mathematics 15 (1963) 433-439.
6. Majorants in variational integration, Canadian Journal of Mathematics 18 (1966) 49-74.
7. A Riemann-type integral of Lebesgue power, Canadian Journal of Mathematics 20 (1968) 79-87.
8. Linear Analysis, Butterworths, London, 1968.
9. Integration by parts, Aequationes Mathematicae 9 (1973) 1-18.
10. The N-variational integral and the Schwarz distributions III, Journal of the London Mathematical Society (2) 6 (1973) 693-700.
11. Integration in product spaces, including Wiener and Feynman integration, Proceedings of the London Mathematical Society (3) 27 (1973) 317-344.
12. Additivity and the Lebesgue limit theorems, The Greek Mathematical Society C. Caratheodory Symposium, 1973, 223-241, (published 1974).
13. Integration, variation and differentiation in division spaces, Proceedings of the Royal Irish Academy, Series A (10) 78 (1978) 69-85.
14. The variation on the real line, Proceedings of the Royal Irish Academy, Series A (1) 79 (1979) 1-10.
15. Generalized Riemann integration and an intrinsic topology, Canadian Journal of Mathematics 32 (1980) 395-413.
16. Division spaces, vector-valued functions and backwards martingales, Proceedings of the Royal Irish Academy, Series A (2) 80 (1980) 217-232.
17. Density integration and Walsh functions, Bulletin of the Malaysian Mathematical Society (2) 5 (1982) 1-19.
18. A problem in two-dimensional integration, Journal of the Australian Mathematical Society, (Series A) 35 (1983) 386-404.
19. The Lebesgue syndrome, Real Analysis Exchange 9 (1983–84) 96-110.
20. The reversal of power and integration, Bulletin of the Institute of Mathematics and its Applications 22 (1986) 60-61.
21. Lectures on the Theory of Integration, World Scientific, Singapore, 1988.
22. A short history of integration theory, South East Asian Bulletin of Mathematics 12 (1988) 75-95.
23. Introduction to the new integrals, New integrals (Coleraine, 1988), 7-9, Lecture Notes in Mathematics, 1419, Springer-Verlag, Berlin, 1990.
24. Integration in infinite-dimensional spaces, New integrals (Coleraine, 1988), 54-65, Lecture Notes in Mathematics, 1419, Springer-Verlag, Berlin, 1990.
25. Stochastic and other functional integrals, Real Analysis Exchange 16 (1990/91) 460-470.
26. The General Theory of Integration, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1991.
27. The integral over product spaces and Wiener's formula, Real Analysis Exchange 17 (1991/92) 737-744.
28. Infinite decimals, Mathematica Japonica 38 (1993) 203-209.
29. Measure spaces and division spaces, Real Analysis Exchange 19 (1993/94) 121-128.
30. The construction of path integrals, Mathematica Japonica 39 (1994) 15-18.
31. Gauge or Kurzweil-Henstock integration. Proceedings of the Prague Mathematical Conference 1996, 117-122, Icaris, Prague, 1997.
32. De La Vallée Poussin’s contributions to integration theory, Charles-Jean de La Vallée Poussin Oeuvres Scientifiques, Volume II, Académie Royale de Belgique, Circolo Matematico di Palermo, 2001, 3-16.
33. Partitioning infinite-dimensional spaces for generalized Riemann integration, (with P. Muldowney and V.A. Skvortsov) Bulletin of the London Mathematical Society, 38 (2006) 795-803.