Upper Bounds for Ratios of Lp Norms On Finite Dimensional Spaces Via Spectral Estimates.
NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CONN NEW LONDON LAB
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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.
- Theoretical Mathematics