Fredholm Index Formula for a Class of Matrix Wiener–Hopf Plus and Minus Hankel Operators with Symmetry

L. P. Castro () and A. S. Silva ()
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L. P. Castro: Universidade de Aveiro
A. S. Silva: Universidade de Aveiro

Chapter 10 in Integral Methods in Science and Engineering, Volume 1, 2010, pp 95-104 from Springer

Abstract: Abstract 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.

Keywords: Fredholm Operator; Hankel Operator; Piecewise Continuous Function; Fredholm Property; Extension Relation (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-0-8176-4899-2_10

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