SciELO - Scientific Electronic Library Online

 
vol.12 número2Fixed point theory for compact absorbing contractions in extension type spacesOn Semisubmedian Functions and Weak Plurisubharmonicity índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.12 no.2 Temuco  2010

http://dx.doi.org/10.4067/S0719-06462010000200014 

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 ]

[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 ]

[6] A. B. Lebre, E. Meister, F. S. Teixeira, Some results on the invertibility of Wiener-Hopf- Hankel Operators, Z. Anal. Anwend. 11 (1992), 57-76.        [ Links ]

[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.