@article { ISI:000280555500005,
	title = {Finite section method for a Banach algebra of convolution type operators on Lp(R) with symbols generated by PC and SO},
	journal = {Integral Equations and Operator Theory},
	volume = {67},
	number = {{4}},
	year = {2010},
	month = {{AUG}},
	pages = {559-600},
	publisher = {{BIRKHAUSER VERLAG AG}},
	type = {{Article}},
	address = {{VIADUKSTRASSE 40-44, PO BOX 133, CH-4010 BASEL, SWITZERLAND}},
	abstract = {<script src={\textquoteright}https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML{\textquoteright}></script><p>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 \(L^p(\mathbb{R})\), \(1 \&lt; p \&lt; \infty\). </p>
},
	keywords = {algebraization, essentialization, Fourier multiplier, homogenization, local principle, slowly oscillating function, two projections theorem}, {Finite section method},
	issn = {{0378-620X}},
	doi = {{10.1007/s00020-010-1784-9}},
	url = {http://www.springerlink.com/content/d7436748p1767u22/},
	author = {Karlovich, Alexei Yu and Mascarenhas, Helena and Santos, Pedro A.}
}
