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
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.
- Michał A. Nowak
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
- Received: 2008-10-15.
- Accepted: 2009-01-13.
