The Fox–Li Operator as a Test and a Spur for Wiener–Hopf Theory

Albrecht Böttcher, Sergei Grudsky and Arieh Iserles ()
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Albrecht Böttcher: TU Chemnitz, Faculty of Mathematics
Sergei Grudsky: CINVESTAV, Department of Mathematics
Arieh Iserles: University of Cambridge, Department of Applied Mathematics and Theoretical Physics Centre for Mathematical Sciences

A chapter in Essays in Mathematics and its Applications, 2012, pp 37-48 from Springer

Abstract: Abstract The paper is a concise survey of some rigorous results on the Fox–Li operator. This operator may be interpreted as a large truncation of a Wiener–Hopf operator with an oscillating symbol. Employing theorems from Wiener–Hopf theory one can therefore derive remarkable properties of the Fox–Li operator in a fairly comfortable way, but it turns out that Wiener–Hopf theory is unequal to the task of answering the crucial questions on the Fox–Li operator.

Keywords: Toeplitz Operator; Eigenvalue Distribution; Rational Symbol; Fredholm Determinant; Nonconstant Entire Function (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-28821-0_3

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DOI: 10.1007/978-3-642-28821-0_3

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