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

abstract

• 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.

authors

• Pourahmadi, Mohsen

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

publisher

• Wiley  Publisher

published in

• Journal of London Mathematical Society  Journal

Digital Object Identifier (DOI)

• 10.1112/jlms/s2-38.1.133

start page

• 133

end page

• 145

volume

• s2-38

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.1112%2Fjlms%2Fs2-38.1.133