Albert Baernstein II

Albert Baernstein II (25 April 1941, Birmingham, Alabama – 10 June 2014, University City, Missouri) was an American mathematician.

Education and career

Baernstein matriculated at the University of Alabama, but after a year there he transferred to Cornell University, where he received his bachelor's degree in 1962. After working for a year for an insurance company, he became a graduate student in mathematics at the University of Wisconsin-Madison, where he received his master's degree in 1964 and Ph.D. in 1968.

Baernstein was from 1968 to 1972 an assistant professor at Syracuse University and from 1972 to 2011 a professor at Washington University in St. Louis, where he retired as professor emeritus.

Contributions

The main focus of Baernstein's was analysis, especially function theory and symmetrization problems. His most important contribution is now called the Baernstein star-function. He originally introduced the star-function to solve an extremal problem posed by Albert Edrei in Nevanlinna theory. Later, the star-function was applied by Baernstein and others to several different extremal problems.

In 1978 he was an Invited Speaker with talk How the *-function solves extremal problems at the ICM in Helsinki. He supervised 15 doctoral students, including Juan J. Manfredi.

Selected publications

• Baernstein, Albert (1969). "A nonlinear Tauberian theorem in function theory". Trans. Amer. Math. Soc. 146: 87–105. doi:10.1090/S0002-9947-1969-0257358-3.
• Baernstein, Albert (1971). "Representations of holomorphic functions by boundary integrals". Trans. Amer. Math. Soc. 160: 27–37. doi:10.1090/S0002-9947-1971-0283182-0.
• Baernstein, Albert (1972). "A representation theorem for functions holomorphic off the real axis". Trans. Amer. Math. Soc. 165: 159–165. doi:10.1090/S0002-9947-1972-0293111-2.
• Baernstein Ii, Albert (1972). "Proof of Edrei's spread conjecture". Bull. Amer. Math. Soc. 78 (2): 277–278. doi:10.1090/S0002-9904-1972-12957-4.
• Baernstein, Albert (1972). "On reflexivity and summability". Studia Mathematica. 42 (1): 91–94. doi:10.4064/sm-42-1-91-94.
• "A generalization of the cos πρ theorem". Trans. Amer. Math. Soc. 193: 181–197. 1974. doi:10.1090/S0002-9947-1974-0344468-7.
• Baernstein, Albert (1974). "Integral means, univalent functions and circular symmetrization". Acta Mathematica. 133 (1): 139–169. doi:10.1007/BF02392144.
• Baernstein, Albert (1976). "Univalence and bounded mean oscillation". The Michigan Mathematical Journal. 23 (3): 217–223. doi:10.1307/mmj/1029001715.
• with Eric T. Sawyer: Embedding and multiplier theorems for H ^p(Rⁿ). Memoirs of the AMS, vol. 318. American Mathematical Soc. 1985. ISBN 9780821823187.
• Baernstein, Albert (1986). "Coefficients of univalent functions with restricted maximum modulus". Complex Variables and Elliptic Equations. 5 (2–4): 225–236. doi:10.1080/17476938608814143.
• "A unified approach to symmetrization". In: Partial differential equations of elliptic type. Cambridge University Press. 1994. pp. 47–91. ISBN 9780521460484.
• "The ∗-function in complex analysis". In: Handbook of Coomplex Analysis: Geometric Function Theory. Vol. 1. North-Holland Amsterdam. 2002. pp. 229–271. ISBN 9780080532813.
• with Daniel Girela and José Ángel Peláez: Baernstein, Albert; Girela, Daniel; Peláez, José Ángel (2004). "Univalent functions, Hardy spaces and spaces of Dirichlet type". Illinois Journal of Mathematics. 48 (3): 837–859. doi:10.1215/ijm/1258131055.