Accession Number:

ADA059027

Title:

Upper Bounds for Ratios of Lp Norms On Finite Dimensional Spaces Via Spectral Estimates.

Descriptive Note:

Technical rept.,

Corporate Author:

NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CONN NEW LONDON LAB

Personal Author(s):

Report Date:

1978-07-18

Pagination or Media Count:

159.0

Abstract:

The L sub 2p norm, for positive integers p, of a real complex polynomial pi sub n of degree at most n is shown to be the positive 2p-th root of a constrained quadratic hermitian form of certain linear operator. The 2p-th root of the spectral radius of this linear operator is shown to give an upper bound for the supremum of the ratio of the L sub 2p norm to the L sub 2 norm of pi sub n, where the supremum is taken over arbitrary real complex polynomials pi sub n. The underlying technique is not restricted to polynomials, and a generalization of these results to arbitrary finite dimensional function spaces which satisfy a certain Non-negativity Condition is presented.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE