Wiener-Hopf Integral Operators with Rational Symbols
In this chapter we study in more detail Wiener-Hopf integral operators with a rational matrix symbol. The technique of Wiener-Hopf factorization is introduced. The fact that the symbols are rational allows us to represent them in a special way. We use this representation to construct explicitly the factors in a canonical Wiener-Hopf factorization. In this way explicit formulas for the inverse and the Fredholm characteristics are obtained. Also convolution operators on a finite interval are analyzed in terms of the special representation of the symbol. An example from linear transport theory illustrates the general theory.
KeywordsMatrix Function Half Plane Generalize Inverse Convolution Operator Real Eigenvalue
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