CUBO A Mathematical Journal Vol.12, N°02, (217-234). June 2010

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

L. P. Castro¹ and A. S. Silva²

Department of Mathematics, Aveiro University, 3810-193 Aveiro, Portugal email: castro@ua.pt email: anabela.silva@ua.pt

ABSTRACT

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.

Key words and phrases: Fredholm property,Fredholm index, Wiener-Hopf operator, Hankel operator, semi-almost periodic matrix-valued function

RESUMEN

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.

Math. Subj. Class.: 47B35, 47A05, 47A12, 47A20, 42A75.

Notas

¹Corresponding author: castro@ua.pt

²Sponsored by Fundação para a Ciência e a Tecnologia (Portugal) under grant number SFRH/BD/38698/2007.

References

[1] G. Bogveradze, Fredholm Theory for Wiener-Hopf plus Hankel Operators, PhD Thesis, University of Aveiro, Aveiro, 2008.        [ Links ]

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[15] D. Sarason, Toeplitz operators with semi-almost periodic symbols, Duke Math. J. 44 (1977), 357-364.        [ Links ]

[16] L. P. Castro and F.-O. Speck, Regularity properties and generalized inverses of delta-related operators, Z. Anal. Anwend. 17 (1998), 577-598        [ Links ]

Received: March 2009.

Revised: May 2009.