Abstract.
We consider the asymptotics of the solutions of large linear systems with Toeplitz matrices generated by a complex valued symbol which is infinitely differentiable, has no zeros on the unit circle, and whose winding number about the origin is zero. The emphasis is on quasi-polynomials as right-hand sides, in which case we show that the central fragment of the solution is asymptotically also a quasi-polynomial. Moreover, we establish asymptotic formulas that give specific components of the solution independently of the other components.
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In the memory of Georgii Semenovich Litvinchuk.
Submitted: April 10, 2007. Accepted: March 10, 2008.
We are greatly indebted to the referees for suggesting substantial simplifications in our original proofs and the constructive advice which helped to improve the exposition.
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Simonenko, I.B., Sukhoverkhov, S. Large Toeplitz Systems with Quasi-polynomial Right-hand Sides. Complex anal.oper. theory 2, 701–707 (2008). https://doi.org/10.1007/s11785-008-0074-x
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DOI: https://doi.org/10.1007/s11785-008-0074-x