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Continuity of the Spectral Factorization Mapping
Author(s) -
Barclay Steven
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610704005575
Subject(s) - factorization , matrix decomposition , logarithm , mathematics , spectral theorem , non negative matrix factorization , matrix (chemical analysis) , spectral analysis , mathematical analysis , pure mathematics , physics , algorithm , eigenvalues and eigenvectors , quantum mechanics , operator theory , materials science , composite material , spectroscopy
It is shown that the matrix spectral factorization mapping is sequentially continuous from L p to H 2p (where 1⩽ p<∞), 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.