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On Some Integral Operators Appearing in Scattering Theory, and their Resolutions

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Spectral Theory and Mathematical Physics

Part of the book series: Latin American Mathematics Series ((LAMSUFSC))

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Abstract

We discuss a few integral operators and provide expressions for them in terms of smooth functions of some natural self-adjoint operators. These operators appear in the context of scattering theory, but are independent of any perturbation theory. The Hilbert transform, the Hankel transform, and the finite interval Hilbert transform are among the operators considered.

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Acknowledgements

S. Richard thanks the Department of Mathematics of the National University of Singapore for its hospitality in February 2019. The authors also thank the referee for suggesting the addition of Remark 2.3. Its content is due to him/her.

The author S. Richard was supported by the grant Topological invariants through scattering theory and noncommutative geometry from Nagoya University, and by JSPS Grant-in-Aid for scientific research (C) no 18K03328, and on leave of absence from Univ. Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France.

The author T. Umeda was supported by JSPS Grant-in-Aid for scientific research (C) no 18K03340.

Author information

Authors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, Japan

    Serge Richard

  2. Department of Mathematical Sciences, University of Hyogo, Shosha, Himeji, Japan

    Tomio Umeda

Authors
  1. Serge Richard
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  2. Tomio Umeda
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Correspondence to Serge Richard .

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Editors and Affiliations

  1. Departamento de Matemáticas y C. C., Universidad de Santiago de Chile, Santiago, Chile

    Pablo Miranda

  2. Institut de Mathématiques de Bordeaux, Talence, Gironde, France

    Nicolas Popoff

  3. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile

    Georgi Raikov

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Richard, S., Umeda, T. (2020). On Some Integral Operators Appearing in Scattering Theory, and their Resolutions. In: Miranda, P., Popoff, N., Raikov, G. (eds) Spectral Theory and Mathematical Physics. Latin American Mathematics Series(). Springer, Cham. https://doi.org/10.1007/978-3-030-55556-6_13

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