Fredholm Index Formula for a Class of Matrix Wiener–Hopf Plus and Minus Hankel Operators with Symmetry
The main goal of this chapter is to obtain a Fredholm index formula for a class of Wiener.Hopf plus and minus Hankel operators which contain a certain symmetry between their Fourier symbols. It is relevant to mention that Wiener. Hopf plus and minus Hankel operators (with and without symmetries) appear in several different kinds of applications [CST04]; therefore, further knowledge about their Fredholm property and index is relevant for both theoretical and applied reasons. In view of this, several works concerning these classes of operators have appeared recently [BoCa06, BoCa, CaSi09, NoCa07]. The Fourier matrix symbols considered in this chapter belong to the C.*algebra of piecewise almost periodic functions. Besides the Fredholm index formula, conditions that ensure the Fredholm property of the operators under study will also be obtained.
KeywordsFredholm Operator Hankel Operator Piecewise Continuous Function Fredholm Property Extension Relation
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- [BoCa]Bogveradze, G., Castro, L.P.: On the Fredholm property and index of Wiener–Hopf plus/minus Hankel operators with piecewise almost periodic symbols. Appl. Math. Inform. Mech., (to appear).Google Scholar