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

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Integral Methods in Science and Engineering, Volume 1

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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.

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References

  1. Bogveradze, G., Castro, L.P.: Wiener–Hopf plus Hankel operators on the real line with unitary and sectorial symbols. Contemp. Math., 414, 77–85 (2006).

    MathSciNet  Google Scholar 

  2. 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).

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  3. Böttcher, A.,Karlovich , Yu.I., Spitkovsky, I.M.: Convolution Operators and Factorization of Almost Periodic Matrix Functions, Birkhäuser, Basel (2002).

    MATH  Google Scholar 

  4. Castro, L.P., Speck, F.-O., Teixeira, F.S.: On a class of wedge diffraction problems posted by Erhard Meister. Operator Theory Adv. Appl., 147, 211–238 (2004).

    MathSciNet  Google Scholar 

  5. Castro, L.P., Silva, A.S.: Invertibility of matrix Wiener–Hopf plus Hankel operators with symbols producing a positive numerical range. Z. Anal. Anwendungen, 28, 119–127 (2009).

    MATH  MathSciNet  Google Scholar 

  6. Nolasco, A.P., Castro, L.P.: A Duduchava-Saginashvili’s type theory for Wiener–Hopf plus Hankel operators. J. Math. Anal. Appl., 331, 329–341 (2007).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Universidade de Aveiro, Aveiro, Portugal

    L. P. Castro & A. S. Silva

Authors
  1. L. P. Castro
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  2. A. S. Silva
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Corresponding author

Correspondence to L. P. Castro .

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Editors and Affiliations

  1. Department of Mathematical , University of Tulsa, South Tucker Drive 800, Tulsa, 74104, U.S.A.

    Christian Constanda

  2. Departamento de Matematica Aplicada, Universidad Cantabria, Santander, 39005, Spain

    M.E. Pérez

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Castro, L.P., Silva, A.S. (2010). Fredholm Index Formula for a Class of Matrix Wiener–Hopf Plus and Minus Hankel Operators with Symmetry. In: Constanda, C., Pérez, M. (eds) Integral Methods in Science and Engineering, Volume 1. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4899-2_10

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