The obituary which follows comprises two parts: A survey of Gordon's life, by his colleague at the University of Canterbury, Professor Brian Woods, and a more technical survey of his mathematical work, contributed by his former colleague at the University of Swansea, Dr Harry Burkill.
Professor Gordon Petersen died on 9 November 1996 at the St John of God Hospital, Halswell, where he had lived for the past six years. He had been Professor of Mathematics at the University of Canterbury from 1965, and Head of the Department of Mathematics from 1967 to 1983, when he retired because of ill-health. He was, in his time, a very considerable ornament to his university, not just for his professional eminence, but also because of a colourful singularity of character not now so common in academic society as it once was.
Gordon was born in San Francisco in 1921, the only child of a father of Danish, and a mother of English stock. He received his early education there, and after taking his bachelor's degree from Stanford University in 1943, he went school-teaching at a boys' boarding school at Deep Springs, a small and remote settlement in Central California. Here he taught not only mathematics, for which he was no doubt well prepared, but also physics. One of his stories of this time had to do with his repeating, with his class, Galileo's famous falling weights experiment. The school was set in a ranch, and so the experiment was conducted by dropping objects of various sizes from the top of a feed silo. He got into trouble with the Matron over this, presumably on safety grounds. At some time in this period, during the war or just after, he was also employed at Moffett Field, a government aeronautical establishment in the San Francisco area. I attempted during his last years at St John of God to find out from him just when this was, and what sort of work he'd done. However, as many of his friends discovered, in conversation Gordon answered very slowly to the helm, like a super-tanker; and all I got from him were amusing and discreditable stories about distinguished aerodynamicists.
Gordon returned to Stanford after these excursions to take his master's degree in 1947, under the supervision of DC Spencer. He then spent two years lecturing at the University of British Columbia, before enrolling at the University of Toronto, taking as his topic functional analysis, with GG Lorentz as his supervisor. His career as a mathematician now began to prosper; he took his doctorate in 1951, in a very short time indeed, and even before this degree had been awarded he had submitted three papers for publication.
There followed a series of one- and two-year posts at universities in the United States and Canada; the University of Manitoba (1951/2), the University of Arizona (1952/3) and the University of Oklahoma (1953/5). In 1955 he was appointed to a two-year Senior Research Fellowship in the University College of Wales at Swansea. When this expired, he returned to the States as an Associate Professor at the University of New Mexico; but in 1959, when a lectureship at Swansea became vacant, he applied for it, despite the considerable financial sacrifice this move entailed. Clearly he had recognized that Swansea offered the most congenial and stimulating environment for him, and again he prospered: He was promoted to Senior Lecturer in 1961, and to Reader in 1964. It was at Swansea that he produced much of the research, on matrix summability theory, for which he is best known, and in 1963 he was awarded the DSc of the University of Wales. He stayed there until in 1965 he was appointed to a chair of Pure Mathematics at the University of Canterbury. He was appointed Head of the Department of Mathematics in 1967, after the departure of Derek Lawden, and remained in this post until, after a stroke in 1983, he retired at the age of 62.
Gordon's life was centred around pure mathematics. (The penumbra was admittedly extensive and varied). The work which he did in matrix summability theory, which was summarized in his well-received book "Regular Matrix Transformations" (1966) gave him an international reputation. He knew, worked with, and was held in respect by an impressive body of mathematicians throughout the world, whom he would visit when on leave, and whose visits to Canterbury greatly enlivened the atmosphere of the department. Even after his translation to Canterbury, at which in the sixties and seventies the teaching load in the department was anomalously high, and where he was involved in administrative work for which he had little taste, and perhaps talent to match, he continued to publish steadily. He promoted research in the department by vigorously fostering the honours and MSc programmes, and under his headship the output of doctorates grew to some respectability. He was devoted to the interests of his students, particularly to those who enrolled in his legendary Honours I analysis class, whom he expected to continue to scale the steepest slopes of rigour and abstraction with him. This devotion verged on possessiveness when, as would at times happen, one of his promising students defected to, say, physics, or electrical engineering. In such cases he suspected underhand dealings by the department concerned, and would mutter darkly.
On the national scene, Gordon was one of the prime movers in establishing the Mathematical Colloquium, the annual meeting of this country's research mathematicians. The idea was mooted by him, he maintained, at a meeting of the Steering Committee in 1965, and the first was held in 1966, the year after his arrival. He also put a great deal of enthusiasm and energy into the first Australasian Mathematical Symposium, which was held in Christchurch in 1978. He was elected to the fellowship of the Royal Society of New Zealand in 1973, and was a member of the London Mathematical Society, the American Mathematical Society, the American Mathematical Association, the Canadian Mathematical Congress, and the New Zealand Mathematical Society.
Beyond mathematics, Gordon had many enthusiasms, which he pursued with zest. He was an avid but informed collector of a surprising variety of things. He had a number of coin collections, centred on different themes; for example, he had coins bearing the heads of each of the Roman emperors; and he knew something discreditable or scandalous about each one of them. This collection can now be seen in the Logie Collection of the Classics Department. Another collection, of Parthian coins, was given to the University of Swansea. He had a remarkable collection of chess-sets. He had many teapots and Toby-jugs, not all of them exquisitely beautiful. He was very keen and knowledgeable in the matter of oriental rugs, which he would pile one on top of the other on the floors of his house, so that at one stage I warned him that if this practice continued, he would have to walk through his rooms stooped. Gordon was an imposing figure (perhaps 1.9m in height, and very broad) and he loved ceremony, enjoying the occasions when, in his magnificent University of Wales Doctor of Science robes, he could appear not just twice as large, but also twice as scarlet, as anyone else. But in less formal occasions his dress could be quite disreputable. His colleagues in the department may have been gratified when he took New Zealand citizenship; but his adoption of the New Zealand bushman and shearer's black woollen singlet for informal wear gave less pleasure.
He loved drama, and he loved to act. I recall of his speaking about his year at the University of Manitoba only once, and that was to reminisce about a production there of a modern Russian play, "He Who gets Slapped" (I had not remembered the author, but Dr Garry Tee, of the University of Auckland, informs me that it was Leonid Andreyev) in which he took a part. A few of his colleagues in Christchurch may recall his cameo role in a production of "A Winter's Tale" that Wendy De La Bere directed. He played the bear, and was terrifying. He also made a very menacing Barnardine in a later production of "Measure for Measure"; this role permitted him to display his famous scowl to very good effect. There is some dispute among his friends as to whether he had any taste, or indeed ear, for music. There is, however, no doubt that one of his most prized possessions was an old-fashioned player-piano, which he would pedal for the entertainment of guests; and he certainly knew the plots of most of the better-known Italian operas, which he treasured, I think, for their ludicrous nature.
Gordon loved to travel, and he travelled widely, and had plans for further travel in his retirement, which in the event he was unable to put into effect. In the early eighties, just before his first stroke, he published privately a number of booklets containing his journals of visits to Denmark and China, both countries dear to his heart. Although he was unable to give these the editing they deserved, they give some insight into his character and tastes. He wrote at this time another little book, which was initially intended to be autobiographical, but which turned out to contain for the most part stories to the credit and discredit of other mathematicians. But in it he paid generous tributes to those from whom he had learnt the craft of mathematical research - these were, notably, Polya at Stanford, Lorentz at Toronto, and Goffman at Oklahoma - and he also paid tribute to some of his best students, particularly those in whose early training he had a part.
The University of Canterbury, and the mathematical community of this country, owe much to Gordon Petersen for his contribution to teaching and research in his subject, and he leaves his colleagues with the memory of a generous and stimulating, if unpredictable and unorthodox, friend.
B A Woods
A summary by H Burkill of his maths work can be seen in Acrobat (pdf) format here.
Bibliography
Books
B1 (with HAZEL PERFECT) Introduction to the theory of groups (translation of the German edition of the original Russian book by P.S. ALEXANDROFF), (Blackie & Son Ltd., London and Glasgow, 1959, iv + 112pp).
B2 Regular matrix transformations (McGraw&endash;Hill Publishing Co. Ltd., London&endash;New York&endash;Toronto, 1966, viii + 142pp).
Papers
1 'Means of Fourier constants', Trans. Roy. Soc. Canada Sect. III 45(1951),33&endash;38. MR13,838.
2 'A note on divergent series', Canad. J. Math. 4(1952),445&endash;454. MR14,368.
3 'Methods of summation', Pacific J. Math. 4(1954),73&endash;77. MR15,618.
4 'Sequences of 0's and 1's and Toeplitz methods of summability', Amer. Math. Monthly 63(1956),174&endash;175. MR17,961.
5 (with R.V. ANDREE) 'Matrix methods of summation, regular for p-adic valuations', Proc. Amer. Math. Soc. 7(1956),250&endash;253. MR17,1201.
6 (with C. GOFFMAN) 'Submethods of regular matrix summability methods', Canad. J. Math. 8(1956),40&endash;46. MR17,727.
6a (with C. GOFFMAN) 'Correction to the paper 'Submethods of regular matrix summability methods", Canad. J. Math. 14(1962)384. MR25#1391.
7 (with C. GOFFMAN) 'Consistent limitation methods', Proc. Amer. Math. Soc. 7(1956),367&endash;369. MR17,1200.
8 'Summability methods and bounded sequences', J. London Math. Soc. 31(1956),324&endash;326. MR18,31.
9 'The iteration of regular matrix methods of summation', Math. Scand. 4(1956),276&endash;280. MR19,29.
10 'Inclusion between limitation methods', Math. Z. 65(1956),494&endash;496. MR18,573.
11 'Almost convergence and two matrix limitation methods', Math. Z. 66(1956),225&endash;227. MR18,889.
12 'Almost convergence and uniformly distributed sequences', Quart. J. Math. Oxford Ser. (2) 7(1956),188&endash;191. MR20#2313a.
13 (with F.R. KEOGH) 'Expansion of a certain infinite product', Math. Gazette 41(1957),129&endash;130. [Not in MR.]
14 'Sets and subseries', Canad. J. Math. 9(1957),223&endash;224. MR19,29.
15 'Consistent summability methods', J. London Math. Soc. 32(1957),62&endash;65. MR18,733.
16 'Sets of consistent summation methods', J. London Math. Soc. 32(1957),377&endash;379. MR19,646.
16a 'Corrigendum: Sets of consistent summation methods', J. London Math. Soc. 33(1958),482. MR21#235.
17 'The norm of iterations of regular matrices', Proc. Cambridge Phil. Soc. 53(1957),286&endash;289. MR19,29.
18 'Sequences of iterations', Math. Z. 68(1957),151&endash;152. MR19,29.
19 'Norms of summation methods', Proc. Cambridge Phil. Soc. 54(1958),354&endash;357. MR20#3400.
20 'Matrix norms'. Quart. J. Math. Oxford Ser. (2) 9(1958),161&endash;168. MR20#4718.
21 (with F.R. KEOGH) 'A universal Tauberian theorem', J. London Math. Soc. 33(1958),121&endash;123. MR19,1049.
22 (with F.R. KEOGH) 'A generalized Tauberian theorem', Canad. J. Math. 10(1958),111&endash;114. MR19,1049.
23 (with F.R. KEOGH and B. LAWTON) 'Well distributed sequences', Canad. J. Math. 10(1958),572&endash;576. MR20#2313b.
24 'Summability methods and unbounded sequences', Math. Scand. 7(1959),170&endash;176. MR22#1778.
25 'Summability and bounded sequences', Proc. Cambridge Phil. Soc. 55(1959),257&endash;261. MR22#153.
26 (with F.R. KEOGH) 'A strengthened form of a theorem of Wiener', Math. Z. 71(1959),31&endash;35. MR23#2001.
27 'Uniformly summable sequences', J. London Math. Soc. 35(1960),449&endash;451. MR23#A1976.
28 'Almost convergence and the Buck&endash;Pollard property', Proc. Amer. Math. Soc. 11(1960),469&endash;477. MR22#2819.
29 'Summability of a class of Fourier series', Proc. Amer. Math. Soc. 11(1960),994&endash;998. MR22#11252.
30 'On functions with positive real part', J. London Math. Soc. 36(1961),49&endash;51. MR26#331.
31 'Matrices and norms', Proc. Cambridge Phil. Soc. 57(1961),271&endash;273. MR22#12330.
32 (with H. BURKILL) 'A relation between Riesz and Riemann summability', Proc. Amer. Math. Soc. 12(1961),453&endash;456. MR20#A2667.
33 (with F.R. KEOGH) 'Riesz summability of subsequences', Quart. J. Math. Oxford Ser. (2) 12(1961),33&endash;44. MR22#11244.
34 'A Tauberian theorem', Math. Z. 79(1962),116&endash;121. MR25#3304.
35 (with A.F. DOWIDAR) 'Summability of subsequences', Quart. J. Math. Oxford Ser. (2) 13(1962),81&endash;89. MR26#523.
36 'An inequality of Hardy's', Quart. J. Math. Oxford Ser. (2) 13(1962),237&endash;240. MR25#4048.
37 'Consistency of summation matrices for unbounded sequences', Quart. J. Math. Oxford Ser. (2) 14(1963),161&endash;169. MR27#3974.
38 (with A.F. DOWIDAR) 'The distribution of sequences and summability', Canad. J. Math. 15(1963),1&endash;10. MR26#1299.
39 (with M.T. McGREGOR) 'On the structure of well distributed sequences', Niew Arch. Wisk. (3) 11(1963),64&endash;67. MR27#3620.
40 (with ANNE C. THOMPSON) 'Infinite linear systems', J. London Math. Soc. 38(1963),335&endash;340. MR27#3652.
41 (with ANNE C. THOMPSON) 'On a theorem of Polya, J. London Math. Soc. 39(1964),31&endash;34. MR28#4270.
42 (with G.S. DAVIES) 'On an inequality of Hardy's, II', Quart. J. Math. Oxford Ser. (2) 15(1964),35&endash;40. MR28#3125.
43 (with ANNE C. BAKER) 'Solvable infinite systems of linear equations', J. London Math. Soc. 39(1964),501&endash;510. MR29#2280.
44 (with ANNE C. BAKER) 'On a theorem of Pólya, II', J. London Math. Soc. 39(1964),745&endash;752. MR29#5017.
45 (with M.T. McGREGOR) 'On the structure of well distributed sequences, II', Nederl. Akad. Wetensch. Proc. Ser. A 67 = Indag. Math. 26(1964),477&endash;487. MR30#1112.
46 'Convergence of infinite linear systems', Nederl. Akad. Wetensch. Proc. Ser. A 67 = Indag. Math. 26(1964),615&endash;619. MR30#105.
47 (with J.W. BAKER) 'Inclusion of sets of regular summability matrices', Proc. Cambridge Phil. Soc. 60(1964),705&endash;712. MR30#1335.
48 (with J.W. BAKER) 'Inclusion of sets of regular summability matrices, II', Proc. Cambridge Phil. Soc. 61(1965),381&endash;394. MR31#534.
49 (with J.W. BAKER) 'Extremal points in summability theory', Compositio Math. 17(1965),190&endash;206. MR33 #7742.
50 'On pairs of summability matrices', Quart. J. Math. Oxford Ser. (2) 16(1965),72&endash;76. MR30#2263.
51 (with J.W. BAKER) 'Inclusion of sets of regular summability matrices, III', Proc. Cambridge Phil. Soc. 62(1966),389&endash;394. MR33#7743.
52 (with M.I. McGREGOR) 'On the structure of well distributed sequences, III', Nederl. Akad. Wetensch. Proc. Ser. A 69 = Indag. Math. 28(1966),42&endash;48. MR33#113.
53 'Extreme points for regular summability matrices', Tohoku Math. J. (2) 18(1966),255&endash;258. MR34#6383.
54 'Regular matrices and bounded sequences', Jber. Deutsch. Math.-Verein, 69(1967),107&endash;151. MR35#2010.
55 'Topology of summability sets', Math. Z. 98(1967),93&endash;103. MR35#2011.
56 'On the structure of well distributed sequences, IV', Nederl. Akad. Wetensch. Proc. Ser. A 70 = Indag. Math. 29(1967),128&endash;131. MR35#157.
57 'On the structure of well distributed sequences, V', Nederl. Akad. Wetensch. Proc. Ser. A 70 = Indag. Math. 29(1967),229&endash;233. MR35#2834.
58 (with J.W. BAKER) 'Summability fields which span the bounded sequences', Proc. Cambridge Phil. Soc. 63(1967),99&endash;106. MR34#6380.
59 'Singularities for matrices and sequences, Math. Z. 103(1968),268&endash;275. MR37#1842.
60 (with A. ZAME) 'Summability properties for the distribution of sequences', Monatsh. Math. 73(1969),147&endash;158. MR39#4541.
61 'Factor sequences for summability matrices', Math. Z. 112(1969),389&endash;392. MR40#6111.
62 (with M. IZUMI and S. IZUMI) 'On Hardy's inequality and its generalization', Tohoku Math. J. (2) 21(1969),601&endash;613. MR41#3693.
63 (with A.P. BAISNAB) 'Metric density and Lusin's theorem', Quart. J. Math. Oxford Ser. (2) 22(1971),457&endash;464. MR45#488.
64 'The relationship of matrix norms to matrix singularities', Math. Z. 127(1972),365&endash;369. MR47#3875.
65 'The algebra of bounded sequences as factor sequences', Nederl. Akad. Wetensch. Proc. Ser. A 75 = Indag. Math. 34(1972),345&endash;349. MR47#9121.
66 'Summability fields which span the bounded sequences densely', Bull. London Math. Soc. 5(1973),187&endash;191. MR48#9162.
66a 'Addendum: Summability fields which span the bounded sequences densely', Bull. London Math. Soc. 7(1975),105. MR54#8077.
67 'Factor sequences and their algebras', Jber. Deutsch. Math. Verein 74(1973),182&endash;188. [Not in MR.]
68 'Regular metric density', Quart. J. Math. Oxford Ser. (2) 24(1973),141&endash;143. MR47#6979.
69 'Factor sequences and their algebras, II', Jber. Deutsch. Math.-Verein, 75(1974),140&endash;143. MR58#1809.
70 'Topology of subsets of the bounded sequences', Proc. Conf. Math. Res. Inst., Oberwolfach, (1974),533&endash;545. MR52#6239.
71 (i) 'A tribute to G.G. Lorentz', Collection of articles dedicated to G.G.Lorentz on the occasion of his sixty&endash;fifth birthday, J. Approximation Theory 13(1975),4&endash;5. MR50#12600.
(ii) 'Tauberian conditions for a class of matrices', ibid., 146&endash;152. MR50#10592.
72 (with T.&endash;O. TO) 'An extension of metric density', Quart. J. Math. Oxford Ser. (2) 27(1976),463&endash;466. MR54#10538.
73 'A sequence algebra associated with distributions', Bull. Austral. Math. Soc. 19(1978),39&endash;49. [Not in MR.]
74 'A Tauberian theorem for Cesàro and Abel summability', Nederl. Akad. Wetensch. Indag. Math. 41(1979),465&endash;468. MR81a:40006.
75 'Pairs of matrices and unbounded sequences', Comment. Math. Prace Mat. 23(1983),101&endash;107. MR85d:40002.
76 'Sequences with the strong Weyl property', J. Nat. Acad. Math. India 2(1984),107&endash;110. MR87d:11044.
77 'The closure of Tauberian sets', Southeast Asian Bull. Math. 14(1990),67&endash;72. MR91f:40007.