ESTONIAN ACADEMY
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eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
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proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2022): 0.9
The life and work of Olof Thorin (1912–2004); pp. 18–25
PDF | doi: 10.3176/proc.2008.1.02

Authors
Lennart Bondesson, Jan Grandell, Jaak Peetre
Abstract
This paper reviews Olof Thorin’s contributions to mathematical analysis, actuarial mathematics, and probability theory, though in reversed order. In probability theory he is known for his path-breaking work on infinite divisibility. In actuarial mathematics he contributed significantly to the ruin problem. However, his international fame very much relies on his work in mathematical analysis and his share in the Riesz–Thorin theorem. Data about his life and some personal recollections are also given.
References

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  2. Steutel, F. W. Some recent results in infinite divisibility. Stochastic Processes Appl., 1973, 1, 125–143.
doi:10.1016/0304-4149(73)90008-2

  3. Thorin, O. On the infinite divisibility of the lognormal distribution. Scand. Actuar. J., 1977, 1977, 121–148.

  4. Thorin, O. On the infinite divisibility of the Pareto distribution. Scand. Actuar. J., 1977, 1977, 31–40.

  5. Thorin, O. Proof of a conjecture of L. Bondesson concerning infinite divisibility of powers of a gamma variable. Scand. Actuar. J., 1978, 1978, 151–164.

  6. Thorin, O. An extension of the notion of a generalized G-convolution. Scand. Actuar. J., 1978, 1978, 141–149.

  7. Bondesson, L. Generalized Gamma Convolutions and Related Classes of Distributions and Densities. Lecture Notes in Statistics, No.~76. Springer-Verlag, New York, 1992.

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11. Lundberg, F. Försäkringsteknisk Riskutjämning. I: Teori. II: Statistik (Insurance technical smoothing of risks). F. Englunds Boktryckeri AB, Stockholm, 1926 (and 1928) (in Swedish).

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14. Thorin, O. An identity in the collective risk theory with some applications. Skand. Aktuarietidskr., 1968, 1968, 26–44.

15. Sparre-Andersen, E. On the collective theory of risk in the case of contagion between the claims. In Transactions of the 15th International Congress of Actuaries, New York, II. 1957, 219–229.

16. Thorin, O. Probabilities of ruin. Scand. Actuar. J., 1982, 1982, 65–102.

17. Thorin, O. and Wikstad, N. Calculation of ruin probabilities when the claim distribution is lognormal. Astin Bull., 1977, 9, 231–246.

18. Peetre, J. On the development of interpolation – Instead of a history three letters. Edited and/or translated by Jaak Peetre. In Function Spaces, Interpolation Theory and Related Topics (Cwikel, M. et al., eds). Walter de Gruyter, Berlin, 2002, 39–48.

19. Peetre, J. Marcel Riesz in Lund. In Function Spaces and Applications (Cwikel, M. et al., eds). Lecture Notes in Mathematics, 1302, Springer-Verlag, Berlin, 1988, 1–10.

20. Thorin, O. An extension of the convexity theorem of M. Riesz. Kungl. Fysiogr. Sällsk. Lund Förh., 1939, 8, No. 14.

21. Thorin, O. Convexity theorems generalizing those of M. Riesz and Hadamard with some applications. Medd. Lunds Univ. Mat. Sem., 1948, 9, 1–58.

22. Peetre, J. Interpolation functors and Banach couples. In Actes du congrès international des mathématiciens, 1970, Nice, France, t. 2. Gauthiers-Villars, Paris, 1971, 373–378.

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24. Riesz, M. Sur les maxima des formes bilinéaires et sur les fonctionelles linéaires. Acta Math., 1927, 49, 465–497.
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25. Littlewood, J. E. A Mathematician’s Miscellany. Methuen, London, 1953.

26. Marcinkiewicz, J. Sur l’interpolation d’opérations. C. R. Acad. Sci., Paris, 1939, 208, 1272–1273.
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