Donald Sarason (nonfiction)

Donald Erik Sarason

Donald Erik Sarason (26 January 1933 – 8 April 2017) was an American mathematician who made fundamental advances in the areas of Hardy space theory and VMO. He was one of the most popular doctoral advisors in the Mathematics Department at UC Berkeley. He supervised 39 Ph.D. theses at UC Berkeley.

Career

Postdoc at the Institute for Advanced Study in 1963–1964, supported by a National Science Foundation Postdoctoral Fellowship. Then Sarason went to the University of California Berkeley as an Assistant Professor (1964–1967), Associate Professor (1967–1970) and until his retirement, Professor (1970–2012).

Accomplishments

Sarason was awarded a Sloan Fellowship for 1969–1971.

Sarason was the author of 78 mathematics publications spanning the fifty years from 1963 to 2013. Sarason was the sole author on 56 of these publications; the other 22 publications were written with a total of 25 different co-authors.

The huge influence of Sarason’s publications on other mathematicians is reflected in unusually high citation rates. Google Scholar shows that Sarason’s publications have been cited over four-thousand times in the mathematical literature.

Sarason wrote an amazing total of 456 reviews for Mathematical Reviews/MathSciNet. These reviews were published from 1970 to 2009.

Teaching awards from UC Berkeley Mathematics Undergraduate Student Association, 2003 and 2006.

At various times, served on the editorial boards of Proceedings of the American Mathematical Society, Integral Equations and Operator Theory, and Journal of Functional Analysis.

Selected works:

• Sarason reproved a theorem of G. Pick on when an interpolation problem can be solved by a holomorphic function that maps the disk to itself. Sarason’s approach not only gave a natural unification of the Pick interpolation problem with the Carathoédory interpolation problem (where the values of phi and its first N-1 derivatives at the origin are given), but it led to the Commutant Lifting theorem of Sz.-Nagy and Foiaş which inaugurated an operator theoretic approach to many problems in function theory.
• Functions of Vanishing Mean Oscillation. Sarason’s work played a major role in the modern development of function theory on the unit circle in the complex plane.
• Function Theory on the Unit Circle. On June 19–23, 1978, Sarason gave a series of ten lectures at a conference hosted by Virginia Polytechnic Institute and State University (now Virginia Tech) on analytic function theory on the unit circle. In these lectures he discussed a number of recent results in the field, bringing together classical ideas and more recent ideas from functional analysis and from the extension of the theory of Hardy spaces to higher dimensions. The lecture notes, entitled Function Theory on the Unit Circle were made available by the math department at VPI. Though only available as a mimeographed document, they circulated widely and were very influential.
• Sub-Hardy Hilbert Spaces in the Unit Disk. This influential book developed the theory of the de Branges–Rovnyak spaces Hb, which were first introduced in de Branges and Rovnyak. Sarason pioneered the abstract treatment of contractive containment and established a fruitful connection between the spaces Hb and the ranges of certain Toeplitz operators. Using reproducing kernel Hilbert space techniques, he gave elegant proofs of the Julia–Carathéodory and the Denjoy–Wolff theorems. Two recent accounts of the theory are Emmanuel Fricain and Javad Mashreghi and Dan Timotin.

Fiction cross-reference

• Crimes against mathematical constants
• Gnomon algorithm
• Gnomon Chronicles
• Mathematician
• Mathematics

Nonfiction cross-reference

• Mathematician (nonfiction)
• Mathematics (nonfiction)

External links

• Donald Saronson @ Wikipedia