Canonical Factorization and Applications

Part of the Operator Theory: Advances and Applications book series (OT, volume 178)


As we have seen in Chapter 1 canonical factorization serves as tool to solve Wiener-Hopf integral equations and their discrete analogues, the block Toeplitz equations. In this chapter the state space factorization method developed in Chapter 2 is used to solve the problem of canonical factorization (necessary and sufficient conditions for its existence) and to derive explicit formulas for its factors. This is done in Section 6.1 for rational matrix functions. The results are applied to invert Wiener- Hopf integral equations (Section 6.2) and block Toeplitz operators (Section 6.3) with a rational matrix symbol.


Unit Circle Open Neighborhood Factorization Theory Canonical Factorization Spectral Subspace 
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© Birkhäuser Verlag AG 2008

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