A note on rearrangements, spectral concentration, and the zero-order prolate spheroidal wavefunction

If the measure of the support of a function f is small, its symmetric decreasing rearrangement f* is more nearly bandlimited to low frequencies than f, while their norms are equal. An immediate corollary is that the time-limited zero-order prolate spheroidal wavefunction is the extremal function for a new optimization problem involving time- and bandlimiting. The result has an application in exploration seismology