Donald Burkholder

Donald Burkholder's AcademicInfluence.com Rankings

Donald Burkholder

Mathematics

#2990

World Rank

#4504

Historical Rank

#1136

USA Rank

Measure Theory

#2594

World Rank

#3108

Historical Rank

#742

USA Rank

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Mathematics

Why Is Donald Burkholder Influential?

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According to Wikipedia, Donald Lyman Burkholder was 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. Burkholder spent most of his professional career as a professor in the Department of Mathematics of the University of Illinois at Urbana-Champaign. After his retirement in 1998, Donald Burkholder remained 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 was a member of the U.S. National Academy of Sciences and a fellow of the American Mathematical Society.

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Donald Burkholder's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Distribution Function Inequalities for Martingales (1973) (740)
Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling. (1962) (602)
Boundary Value Problems and Sharp Inequalities for Martingale Transforms (1984) (358)
Extrapolation and interpolation of quasi-linear operators on martingales (1970) (337)
Explorations in martingale theory and its applications (1991) (254)
Chapter 6 - Martingales and Singular Integrals in Banach Spaces (2001) (201)
Martingales and Fourier analysis in Banach spaces (1986) (200)
Sharp inequalities for martingales and stochastic integrals (1988) (183)
A maximal function characterization of the class (1971) (133)
A Geometrical Characterization of Banach Spaces in Which Martingale Difference Sequences are Unconditional (1981) (128)
Exit times of Brownian motion, harmonic majorization, and Hardy spaces☆ (1977) (112)
Distribution function inequalities for the area integral (1972) (78)
A proof of Pełczyński's conjecture for the Haar system (1988) (56)
Successive Conditional Expectations of an Integrable Function (1962) (49)
Iterates of conditional expectation operators (1961) (48)
The best constant in the Davis inequality for the expectation of the martingale square function (2001) (48)
Sufficiency in the Undominated Case (1961) (39)
Martingale transforms and the geometry of Banach spaces (1981) (38)
On a Class of Stochastic Approximation Processes (1956) (37)
Optimum Properties and Admissibility of Sequential Tests (1963) (36)
A Sharp and Strict $L^p$-Inequality for Stochastic Integrals (1987) (35)
Differential subordination of harmonic functions and martingales (1989) (33)
An elementary proof of an inequality of R (1985) (33)
Independent Sequences with the Stein Property (1968) (32)
A nonlinear partial differential equation and the unconditional constant of the Haar system in $L^p$ (1982) (28)
Maximal inequalities as necessary conditions for almost everywhere convergence (1964) (27)
Strong Differential Subordination and Stochastic Integration (1994) (26)
A Sharp Inequality for Martingale Transforms (1979) (23)
One-sided maximal functions and Hp (1975) (22)
Review: Gilles Pisier, The volume of convex bodies and Banach space geometry (1991) (16)
Boundary behaviour of harmonic functions in a half-space and brownian motion (1973) (14)
Sharp norm comparison of Martingale maximal functions and stochastic integrals (1997) (14)
Discussion on Professor Kingman's Paper (1973) (8)
Stopping Times and Directed Processes, Encyclopedia of Mathematics and its Applications; Volume 47 - G. A. Edgar; L. Sucheston. (1994) (7)
Boundary value estimation of the range of an analytic function. (1978) (6)
Weak inequalities for exit times and analytic functions (1979) (5)
On the Order Structure of the Set of Sufficient Subfields (1962) (5)
$H^p$ spaces and exit times of Brownian motion (1975) (2)
SHARP MARTINGALE INEQUALITIES AND APPLICATIONS TO RIESZ TRANSFORMS ON MANIFOLDS, LIE GROUPS AND GAUSS SPACE (2015) (1)
Selected Works of Donald L. Burkholder (2011) (1)
On the Existence of a Best Approximation of One Distribution Function by Another of a Given Type (1959) (1)
Approximation of ¹-bounded martingales by martingales of bounded variation (1978) (1)
Joseph Leo Doob, 1910–2004 (2005) (0)
Joseph Leo Doob (1910-2004) (2006) (0)
Book reviews (1997) (0)
AND STOCHASTIC INTEGRATION (2016) (0)
Bibliography: Publications of J. L. Doob (2009) (0)
PEM volume 33 issue 3 Cover and Back matter (1990) (0)
PEM volume 35 issue 3 Cover and Back matter (1992) (0)
DEVELOPMENT OF HIGH TEMPERATURE AIRCRAFT ELECTRICAL SYSTEM (1961) (0)
Comments on [5], [14], [22], [30], and [31] (2006) (0)
EFFECT ON THE MINIMAL COMPLETE CLASS OF TESTS OF CHANGES IN THE TESTING PROBLEM (1960) (0)
Book reviews (1994) (0)
I. Novikov and E. Semenov,Haar Series and Linear Operators (1998) (0)

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Donald Burkholder's Academic­Influence.com Rankings