#### Milestone Year

### 1976

#### Trace Formulas

A famous theorem of Gabor Szego expresses the growth of the determinant
of an n × n matrix with ij entry equal to the i-j th Fourier coefficient
of a nice function as n gets large, in terms of the function itself. In
1954, Mark Kac obtained a continuous analogue of Szego's theorem for a
class of integral operators considered on an increasing sequence of
intervals.

Some 20-plus years later, while trying to understand Kac's paper, a
Weizmann mathematician realized that (by invoking the Paley-Wiener
theorem) Kac's theorem could be reformulated in terms of trace formulas
of projections onto spaces of entire functions of exponential type that
are square summable with respect to Lebesgue measure. This led to a number
of generalizations in which functions were replaced by vector valued
functions, and Lebesgue measure was replaced by a wider class of weights.
These and other related directions were pursued over the years, partially
in collaboration with students and postdoctoral fellows.