I have been looking for a result on interpolation of non-bandlimited signals.

It is well known the WKS sampling theorem which states that a bandlimited signal can be reconstructed as

f(t)=sum{f(nT)sinc(T^-1(t-nt))}

however, what happens if we compute this very series for a non-bandlimited signal whose spectrum is L1 and not L2? For signals whose spectrum is L1 there is a result due to J.L Brown (JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 18, 75-84 (1967)) which asserts that such series uniformly approximates f(t).

So, any clues?