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.