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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.12 no.2 Temuco  2010 

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: email:


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


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.


1Corresponding author:

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


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

[2] G. Bogveradze and L. P. Castro, Wiener-Hopf plus Hankel operators on the real line with unitary and sectorial symbols, Contemp. Math. 414 (2006), 77-85.        [ Links ]

[3] L. P. Castro, F.-O. Speck and F. S. Teixeira, A direct approach to convolution type operators with symmetry, Math. Nachr. 269-270 (2004), 73-85.        [ Links ]

[4] L. P. Castro and A. S. Silva, Invertibility of matrix Wiener-Hopf plus Hankel operators with symbols producing a positive numerical range, Z. Anal. Anwend. 28 (2009), 119-127.        [ Links ]

[5] T. Ehrhardt, Factorization Theory for Toeplitz plus Hankel Operators and Singular Integral Operators with Flip, Habilitation Thesis, Technischen Universitität Chemnitz, Chemnitz, 2004.        [ Links ]

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[7] A. P. Nolasco, Regularity Properties of Wiener-Hopf-Hankel Operators. PhD Thesis, University of Aveiro, Aveiro, 2007.        [ Links ]

[8] A. P. Nolasco and L. P. Castro, A Duduchava-Saginashvili's type theory for Wiener-Hopf plus Hankel operators, J. Math. Anal. Appl. 331 (2007), 329-341.        [ Links ]

[9] L. P. Castro and D. Kapanadze, Exterior wedge diffraction problems with Dirichlet, Neumann and Impedance boundary conditions, Acta Appl. Math., 110 (2010), 289-311.        [ Links ]

[10] L. P. Castro, F.-O. Speck and F. S. Teixeira, Explicit solution of a Dirichlet-Neumann wedge diffraction problem with a strip, J. Integral Equations Appl. 15 (2003), 359-383.        [ Links ]

[11] L. P. Castro, F.-O. Speck and F. S. Teixeira, On a class of wedge diffraction problems posted by Erhard Meister, Oper. Theory Adv. Appl. 147 (2004), 211-238.        [ Links ]

[12] E. Meister, F.-O. Speck and F. S. Teixeira, Wiener-Hopf-Hankel operators for some wedge diffraction problems with mixed boundary conditions, J. Integral Equations Appl. 4 (1992), 229-255.        [ Links ]

[13] G. Bogveradze and L. P. Castro, On the Fredholm index of matrixWiener-Hopf plus/minus Hankel operators with semi-almost periodic symbols, Oper. Theory Adv. Appl. 181 (2008), 143-158.        [ Links ]

[14] A. Böttcher, Yu. I. Karlovich and I. M. Spitkovsky, Convolution Operators and Factorization of Almost Periodic Matrix Functions, Birkhäuser, Basel, 2002.        [ Links ]

[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.

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