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

In: Integral Methods in Science and Engineering, Volume 1

Author

Listed:
  • L. P. Castro

    (Universidade de Aveiro)

  • A. S. Silva

    (Universidade de Aveiro)

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.

Suggested Citation

  • L. P. Castro & A. S. Silva, 2010. "Fredholm Index Formula for a Class of Matrix Wiener–Hopf Plus and Minus Hankel Operators with Symmetry," Springer Books, in: Christian Constanda & M.E. Pérez (ed.), Integral Methods in Science and Engineering, Volume 1, chapter 10, pages 95-104, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-4899-2_10
    DOI: 10.1007/978-0-8176-4899-2_10
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