Jspectral factorization and equalizing vectors
Iftime, O.V. and Zwart, H.J. (2000) Jspectral factorization and equalizing vectors. [Report]

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Abstract:  For the Wiener class of matrixvalued functions we provide necessary and sufficient conditions for the existence of a spectral factorization. One of these conditions is in terms of equalizing vectors. A second one states that the existence of a spectral factorization is equivalent to the invertibility of the Toeplitz operator associated to the matrix to be factorized. Our proofs are simple and only use standard results of general factorization theory. Note that we do not use a state space representation of the system. However, we make the connection with the known results for the PritchardSalamon class of systems where an equivalent condition with the solvability of an algebraic Riccati equation is given. For Rieszspectral systems another necessary and sufficient conditions for the existence of a spectral factorization in terms of the Hamiltonian is added. 
Item Type:  Report 
Additional information:  Imported from MEMORANDA 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
Research Group:  
Link to this item:  http://purl.utwente.nl/publications/65732 
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