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The Behaviour of Legendre And Ultraspherical Polynomials in Lp -Spaces

  • N. J. Kalton (a1) and L. Tzafriri (a1)
Abstract

We consider the analogue of the λ(p)problem for subsets of the Legendre polynomials or more general ultraspherical polynomials. We obtain the “best possible” result that if 2 < p < 4 then a random subset of N Legendre polynomials of size N4/p-1 spans an Hilbertian subspace. We also answer a question of König concerning the structure of the space of polynomials of degree n in various weighted Lp -spaces.

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The first author was supported by NSF grant DMS-9500125. The second author was partially supported by the Landau Center for Research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation (Germany).

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References
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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