CONTINUITY OF THE SPECTRAL FACTORIZATION MAPPING

STEVEN BARCLAY

doi:10.1112/S0024610704005575

Abstract

It is shown that the matrix spectral factorization mapping is sequentially continuous from $\LL^p$ to $\HH^{2p}$ (where $1\,{\le}\, p\,{<}\,\infty$), under the additional assumption of uniform integrability of the logarithms of the spectral densities to be factorized. It is shown, moreover, that this condition is necessary for continuity, as well as sufficient.

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CONTINUITY OF THE SPECTRAL FACTORIZATION MAPPING

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CONTINUITY OF THE SPECTRAL FACTORIZATION MAPPING

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