Abstract
In this chapter we study in more detail block Toeplitz operators defined by rational functions. The technique of Wiener-Hopf factorization is employed. The fact that the defining functions are rational allows us to represent the corresponding Toeplitz operators in a special way. We use this representation to construct explicitly the factors in a canonical Wiener-Hopf factorization. This yields explicit formulas for the inverse and the Fredholm characteristics. The results obtained here may be viewed as discrete analogues of the inversion and Fredholm theorems for Wiener-Hopf integral operators in Chapter XIII.
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© 1993 Springer Basel AG
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Gohberg, I., Kaashoek, M.A., Goldberg, S. (1993). Toeplitz Operators Defined by Rational Matrix Functions. In: Classes of Linear Operators Vol. II. Operator Theory Advances and Applications, vol 63. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8558-4_6
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DOI: https://doi.org/10.1007/978-3-0348-8558-4_6
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9679-5
Online ISBN: 978-3-0348-8558-4
eBook Packages: Springer Book Archive