Opuscula Math. 29, no. 3 (2009), 271-288
http://dx.doi.org/10.7494/OpMath.2009.29.3.271

Opuscula Mathematica

# Approximation methods for a class of discrete Wiener-Hopf equations

Michał A. Nowak

Abstract. In this paper, we consider approximation methods for operator equations of the form $Au + Bu = f,$ where $$A$$ is a discrete Wiener-Hopf operator on $$l_p$$ ($$1 \leq p \lt \infty$$) which symbol has roots on the unit circle with arbitrary multiplicities (not necessary integers). Conditions on perturbation $$B$$ and $$f$$ are given in order to guarantee the applicability of projection-iterative methods. Effective error estimates, and simultaneously, decaying properties for solutions are obtained in terms of some smooth spaces.

Keywords: projection methods, iterative methods, discrete Wiener-Hopf equations, Toeplitz operators.

Mathematics Subject Classification: 65J10, 65Q05.

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• Michał A. Nowak
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland