Best Approximations in Lp (d ) and Prediction Problems of Szeg, Kolmogorov, Yaglom, and Nakazi Academic Article uri icon


  • For a non-negative weight function W we prove a general prediction theorem which for a sub-space M Lp(w), 1< p <, and h Lprovides formulae expressing inffM||h-f||p, wand PMh (metric projection) in terms of inffM||h-f||q, wand PNh, where N (related to M) is a subspace of Lq(W8), 1/p+1/q=1 and s = - l/(p- 1). It is shown that this general prediction theorem subsumes and generalizes to p 2 the prediction theorems of Szego (1918), Kolmogorov (1941), Yaglom (1963), and Nakazi (1984). 1988 Oxford University Press.

published proceedings

  • Journal of the London Mathematical Society

author list (cited authors)

  • Miamee, A. G., & Pourahmadi, M.

citation count

  • 21

complete list of authors

  • Miamee, AG||Pourahmadi, Mohsen

publication date

  • January 1988