On the inversion of higher order Wiener-Hopf operators. (English) Zbl 0873.47015
Summary: It is known that the Banach algebra generated by classical Wiener-Hopf operators on the half-line is an algebra with symbol. This concept yields, in particular, a Fredholm criterion and an index formula. In the present paper, we introduce a different symbol for the finitely generated algebra. It is based on matricially coupling of operators and implies a representation of a generalized inverse in terms of matrix factorization. Some examples demonstrate how to use these results for a discussion of properties of the solution of singular equations.
MSC:
| 47B35 | Toeplitz operators, Hankel operators, Wiener-Hopf operators |
Keywords:
Banach algebra; classical Wiener-Hopf operators; algebra with symbol; Fredholm criterion; index formula; singular equationsReferences:
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