Abstract
We prove necessary and sufficient conditions for the applicability of the finite section method to an arbitrary operator in the Banach algebra generated by the operators of multiplication by piecewise continuous functions and the convolution operators with symbols in the algebra generated by piecewise continuous and slowly oscillating Fourier multipliers on \({L^p(\mathbb {R})}\), 1 < p < ∞.
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To the memory of Professor Israel Gohberg (23.08.1928–12.10.2009)
After this paper was submitted, we received the sad news that Israel Gohberg has passed away on October 12, 2009. Professor Gohberg has left his imprint on many areas of analysis, including the theory of convolution type operators and projection methods for their solution. We would like to dedicate this contribution to him with admiration.
This work is partially supported by the grant FCT/FEDER/POCTI/MAT/59972/2004.
An erratum to this article can be found at http://dx.doi.org/10.1007/s00020-010-1855-y
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Karlovich, A.Y., Mascarenhas, H. & Santos, P.A. Finite Section Method for a Banach Algebra of Convolution Type Operators on \({L^p(\mathbb R)}\) with Symbols Generated by PC and SO . Integr. Equ. Oper. Theory 67, 559–600 (2010). https://doi.org/10.1007/s00020-010-1784-9
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DOI: https://doi.org/10.1007/s00020-010-1784-9