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Journal of the London Mathematical Society (1)

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CONTINUITY OF THE SPECTRAL FACTORIZATION MAPPING
STEVEN BARCLAY
Journal:

Journal of the London Mathematical Society / Volume 70 / Issue 3 / December 2004

Published online by Cambridge University Press:

03 December 2004, pp. 763-779

Print publication:

December 2004
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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.