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

In: Essays in Mathematics and its Applications

Author

Listed:
  • 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)

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.

Suggested Citation

  • Albrecht Böttcher & Sergei Grudsky & Arieh Iserles, 2012. "The Fox–Li Operator as a Test and a Spur for Wiener–Hopf Theory," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Essays in Mathematics and its Applications, edition 127, pages 37-48, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-28821-0_3
    DOI: 10.1007/978-3-642-28821-0_3
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