The behaviour of Legendre and ultraspherical polynomials in L-p-spaces

Authors
Kalton, NJ Tzafriri, L
Citation
Nj. Kalton et L. Tzafriri, The behaviour of Legendre and ultraspherical polynomials in L-p-spaces, CAN J MATH, 50(6), 1998, pp. 1236-1252
Citations number
15
Categorie Soggetti
Mathematics
Journal title
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
ISSN journal
0008414X → ACNP
Volume
50
Issue
6
Year of publication
1998
Pages
1236 - 1252
Database
ISI
SICI code
0008-414X(199812)50:6<1236:TBOLAU>2.0.ZU;2-8
Abstract
We consider the analogue of the Lambda(p)-problem for subsets of the Legend re polynomials or more general ultraspherical polynomials. We obtain the "b est possible" result that if 2 < p < 4 then a random subset of N Legendre p olynomials of size N-4/(p-1) spans an Hilbertian subspace. We also answer a question of Konig concerning the structure of the space of polynomials of degree rr in various weighted L-p-spaces.