Continuity of the spectral factorization on a vertical strip |
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| Authors: | Birgit Jacob Joseph Winkin Hans Zwart |
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| Affiliation: | a School of Mathematics, University of Leeds, Leeds LS2 9JT, UK;b Facultés Universitaires Notre-Dame de la Paix, Department of Mathematics, Rempart de la Vierge, 8, B-5000 Namur, Belgium;c University of Twente, Faculty of Mathematical Sciences, P.O. Box 217, NL-7500 AE Enschede, Netherlands |
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| Abstract: | The continuity of the mapping which associates a spectral factor to a spectral density is investigated. This mapping can be defined on several classes of spectral densities and spectral factors. For the usual largest class of spectral densities, i.e., essential bounded functions on the imaginary axis that are bounded away from zero, it is known that this mapping is not continuous. It is shown here that for slightly smaller, but still generic class the mapping becomes continuous. |
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| Keywords: | Spectral density Spectral factor Coercivity Approximate spectral factorization |
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