Prof. Avraham Melkman

Denote by B(o, T) the class of entire functions of exponential type o which are bounded by 1 on the real axis outside (-T, T). It is shown that this class, considered as a subset of C[-T, T], has
approximate dimension 2oT/r in analogy to the Landau-Pollak-Slepian dimension theorem. More generally, the optimal subspaces and corresponding worst functions for the n-widths of B(o, T) are characterized.
Prominently featured is the fact that it is possible to achieve the n-widths via interpolation, provided the sampling points are adroitly chosen. However, the interpolating functions differ from the standard ones.