Donald Burkholder

Donald L. Burkholder (born 1927) is an American mathematician known for his contributions to probability theory, particularly the theory of martingales. The Burkholder–Davis–Gundy inequality is co-named after him. Donald Burkholder is a Professor Emeritus in the Department of Mathematics of the University of Illinois at Urbana-Champaign and a CAS Professor Emeritus of Mathematics at the Center for Advanced Study, University of Illinois at Urbana-Champaign. He is a member of the U.S. National Academy of Sciences.

Biographical data

Burkholder received a PhD in Statistics in 1955 from the University of North Carolina at Chapel Hill, under the direction of W. Hoeffding.^[1] He was appointed an Assistant Professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign in 1955^[2] where he remained until his retirement in 1998.^[3] He was promoted to Associate Professor in 1960,^[4] became a Professor in the department in 1964 and was appointed as Professor at the Center for Advanced Study at UIUC in 1978.^[3]

Burkholder delivered an invited lecture at the International Congress of Mathematicians in 1970, a Wald Lecture at the Institute of Mathematical Statistics in 1971, a Mordell Lecture at Cambridge University in 1986, and a Zygmund Lecture at the University of Chicago in 1988.^[5]

Donald Burkholder was elected a member of the U.S. National Academy of Sciences in 1992.^[6][7] The same year he was elected a fellow of the American Academy of Arts and Sciences.^[8] On December 20, 2010 Burkholder was elected a Fellow of the American Association for the Advancement of Science for "distinguished contributions to probability theory, particularly the theory of martingales, and his work in stochastic processes, functional analysis, and Fourier analysis."^[9][10]

In 2009 Burkholder was named a SIAM Fellow by the Society for Industrial and Applied Mathematics "for advances in martingale transforms and applications of probabilistic methods in analysis".^[11][12]

Burkholder is a past Editor (1964–1967) of the journal Annals of Mathematical Statistics.^[13] He served as the President of the Institute of Mathematical Statistics in 1975-76.^[5] He is a Fellow of the Institute of Mathematical Statistics.^[14]

Selected publications

• Burkholder, D. L.; Gundy, Richard F., Extrapolation and interpolation of quasi-linear operators on martingales. Acta Mathematica, vol. 124 (1970), pp. 249–304
• Burkholder, Donald L., Inequalities for operators on martingales. Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2, pp. 551–557. Gauthier-Villars, Paris, 1971.
• Burkholder, Donald L., Distribution function inequalities for martingales, Annals of Probability, vol. 1 (1973), pp. 19–42
• Burkholder, Donald L., A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional. Annals of Probability, vol. 9 (1981), no. 6, pp. 997–1011
• Burkholder, Donald L., Explorations in martingale theory and its applications. École d'Été de Probabilités de Saint-Flour XIX-1989, pp. 1–66, Lecture Notes in Mathematics, vol. 1464, Springer-Verlag, Berlin, 1991

See also

• Martingales
• Burkholder–Davis–Gundy inequality

References

1. ^ Ph.D.s in Statistics, Department of Statistics and Operations Research, University of North Carolina at Chapel Hill. Accessed January 2010
2. ^ News and Notices, The American Mathematical Monthly, Vol. 63, No. 2 (Feb., 1956), pp. 137-141
3. ^ ^{a b} Math Times, Spring 1998 issue, Department of Mathematics, University of Illinois at Urbana-Champaign. Accessed January 12, 2010.
4. ^ News and Notices, The American Mathematical Monthly, Vol. 68, No. 3 (Mar., 1961), pp. 313-318
5. ^ ^{a b} Faculty Honors. Department of Mathematics, University of Illinois at Urbana-Champaign. Accessed January 12, 2010.
6. ^ 59 Are Chosen for National Academy of Sciences. New York Times, May 10, 1992. Accessed January 12, 2010.
7. ^ Burkholder, Donald L. bio page, National Academy of Sciences. Accessed January 12, 2010. Election citation: "During the last twenty years, Burkholder has been the leader in martingale transforms and applications of probabilistic methods to a large variety of areas in analysis, such as harmonic and analytic functions, singular integrals and Banach space classifications. He obtained wide and striking extensions of Paley's ideas in harmonic analysis of more than 30 years before."
8. ^ Math Times, Fall 1992 issue, Department of Mathematics, University of Illinois at Urbana-Champaign, p. 4
9. ^ AAAS Members Elected as Fellows, American Association for the Advancement of Science. Accessed January 13, 2011
10. ^ Illinois mathematician elected fellow of AAAS, News Bureau, University of Illinois. Accessed January 13, 2011
11. ^ SIAM announces new Fellows. IMS Bulletin, vol. 38 (2009), no. 5, Institute of Mathematical Statistics. Accessed January 12, 2010
12. ^ SIAM names 193 Fellows for key contributions to applied mathematics and computational science. News of SIAM, May 1, 2009, Society for Industrial and Applied Mathematics. Accessed January 12, 2010
13. ^ Past Editors of IMS Journals. Institute of Mathematical Statistics. Accessed January 12, 2010
14. ^ IMS Fellows, Institute of Mathematical Statistics. Accessed January 2010.

External links

• Burkholder's personal web page, Department of Mathematics, University of Illinois at Urbana-Champaign
• Donald L. Burkholder, CAS Professor Emeritus of Mathematics, Center for Advanced Study, University of Illinois at Urbana-Champaign
• Donald Burkholder at the Mathematics Genealogy Project

Persondata
Name	Burkholder, Donald L.
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Date of birth	1927
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Date of death
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