Fredholm Property of Matrix Wiener-Hopf plus and minus Hankel Operators with Semi-Almost Periodic Symbols

• L. P Castro ^[1] ; A. S. Silva ^[1]
  1. [1] Aveiro University Department of Mathematics
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 12, Nº. 2, 2010, págs. 217-234
• Idioma: inglés
• DOI: 10.4067/S0719-06462010000200014
• Enlaces
  • Texto completo
• Resumen
  • español

    Presentaremos condiciones suficientes para garantizar la propiedad de Fredholm de operadores de tipo Wiener-Hopf más y menos Hankel con diferentes símbolos de Fourier matriciales en la C*-álgebra de elementos semi-casi periódicos. Además, bajo tales condiciones, obtendremos una fórmula para la suma de los ´ındices de Fredholm de estos operadores Wiener-Hopf más Hankel y Wiener-Hopf menos Hankel. Algunos ejemplos son dados para ilustrar los resultados del artículo.

  • English

    We will present sufficient conditions for the Fredholm property of Wiener-Hopf plus and minus Hankel operators with different Fourier matrix symbols in the C*-algebra of semialmost periodic elements. In addition, under such conditions, we will derive a formula for the sum of the Fredholm indices of theseWiener-Hopf plus Hankel and Wiener-Hopf minus Hankel operators. Some examples are provided to illustrate the results of the paper.

• Referencias bibliográficas
  • Bogveradze, G. (2008). Fredholm Theory for Wiener-Hopf plus Hankel Operators. PhD Thesis, University of Aveiro. Aveiro.
  • Bogveradze, G,Castro, L. P. (2006). Wiener-Hopf plus Hankel operators on the real line with unitary and sectorial symbols. Contemp. Math....
  • Castro, L. P,Speck, F.-O,Teixeira, F. S. (2004). A direct approach to convolution type operators with symmetry. Math. Nachr. 269-270
  • Castro, L. P,Silva, A. S.. (2009). Invertibility of matrix Wiener-Hopf plus Hankel operators with symbols producing a positive numerical range....
  • Ehrhardt, T. (2004). Factorization Theory for Toeplitz plus Hankel Operators and Singular Integral Operators with Flip: Habilitation Thesis....
  • Lebre, A. B,Meister, E,Teixeira, F. S. (1992). Some results on the invertibility of Wiener-Hopf- Hankel Operators. Z. Anal. Anwend. 11. 57-76
  • Nolasco, A. P. (2007). Regularity Properties of Wiener-Hopf-Hankel Operators: PhD Thesis. University of Aveiro. Aveiro.
  • Nolasco, A. P,Castro, L. P. (2007). A Duduchava-Saginashvili’s type theory for Wiener-Hopf plus Hankel operators. J. Math. Anal. Appl. 331....
  • Castro, L. P,Kapanadze, D. (2010). Exterior wedge diffraction problems with Dirichlet, Neumann and Impedance boundary conditions. Acta Appl....
  • Castro, L. P,Speck, F.-O,Teixeira, F. S. (2003). Explicit solution of a Dirichlet-Neumann wedge diffraction problem with a strip. J. Integral...
  • Castro, L. P,Speck, F.-O.,Teixeira, F. S.. (2004). On a class of wedge diffraction problems posted by Erhard Meister. Oper. Theory Adv. Appl....
  • Meister, E,Speck, F.-O,Teixeira, F. S. (1992). Wiener-Hopf-Hankel operators for some wedge diffraction problems with mixed boundary conditions....
  • Bogveradze, G,Castro, L. P. (2008). On the Fredholm index of matrixWiener-Hopf plus/minus Hankel operators with semi-almost periodic symbols....
  • Böttcher, Yu., A,Karlovich, I,Spitkovsky, I. M. (2002). Convolution Operators and Factorization of Almost Periodic Matrix Functions. Birkhäuser....
  • Sarason, D. (1977). Toeplitz operators with semi-almost periodic symbols. Duke Math. J. 44. 357-364
  • Castro, L. P.,Speck, F.-O. (1998). Regularity properties and generalized inverses of delta-related operators. Z. Anal. Anwend. 17. 577-598