Topic #11 --------------- OP-SF NET ---------------- November 9, 1995

From: Walter Van Assche
walter.vanassche@wis.kuleuven.ac.be

Subject: **Death of Joe L. Ullman
**

(This topic was borrowed from the OP-SF Newsletter, October 1995. Look there for some more mathematical details and for references.)

Joe L. Ullman, Professor Emeritus of the University of Michigan, died on Monday, September 11, 1995 at the age of 72. Ullman is known for his work in logarithmic potential theory and orthogonal polynomials, and he has made important contributions to the theory of orthogonal polynomials on the infinite interval and Chebyshev quadrature (with equal weights at every node). Joe was a student of Gabor Szego under whose supervision he prepared his Ph.D. thesis on "Studies of Faber polynomials" at Stanford University in 1949.

Ullman was born January 30, 1923 in Buffalo, New York. He received his B.A. from the University of Buffalo in 1942. He fought in World War II, receiving a purple heart, and later served as an instructor of mathematics at army schools in Czechoslovakia and France. After his Ph.D. he joined the faculty of the Department of Mathematics at the University of Michigan, where he taught and did his research for 44 years.

Ullman's name will forever be connected with Ullman's criterion for regular asymptotic behaviour of orthogonal polynomials and regular zero behaviour. Ullman's criterion for orthogonal polynomials with respect to a positive measure on [-1,1] is that the the minimal carrier capacity of the measure is equal to the capacity of its support, which is 1/2 if the support is [-1,1]. The asymptotic distribution of the contracted zeros of Freud-type orthogonal polynomials is given by a measure with explicit density which is known as the Ullman measure in view of certain results of Ullman. He also showed that equal weight quadrature (Chebyshev quadrature) is possible on an infinite interval, which is a rather surprising result.

At home he was always ready to help his wife Barbara at their little farm (with a dozen sheep and some goats), but most of us will remember him for his love of classical analysis and his interesting research, as can be judged from the following quote from the book by Stahl and Totik: "It was especially J. Ullman who systematically studied different bounds and asymptotics on orthogonal polynomials with respect to arbitrary measures on [-1,1], and we owe a lot to his research and personally to him for initiating and keeping alive the subject".

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revised February 23, 1996