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Eigenvalue Bounds for Self-Adjoint Eigenvalue Problems

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Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations

Part of the book series: Springer Series in Computational Mathematics ((SSCM,volume 53))

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Abstract

Eigenvalue problems Au = λu with a self-adjoint operator A are ubiquitous in mathematical analysis and mathematical physics. A particularly rich field of application is formed by linear differential expressions which can be realized operator-theoretically by self-adjoint operators. Often such eigenvalue problems arise from wave- or Schrödinger-type equations after separation of the time variable, i.e. by a standing-wave ansatz. Possibly the most important physical application is quantum physics, but also other fields like electro-dynamics (including optics) or statistical mechanics are governed by partial differential operators and related eigenvalue problems.

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Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University, Fukuoka, Japan

    Mitsuhiro T. Nakao

  2. Faculty of Mathematics, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Michael Plum

  3. Research Institute for Information Technology, Kyushu University, Fukuoka, Japan

    Yoshitaka Watanabe

Authors
  1. Mitsuhiro T. Nakao
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  2. Michael Plum
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  3. Yoshitaka Watanabe
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Nakao, M.T., Plum, M., Watanabe, Y. (2019). Eigenvalue Bounds for Self-Adjoint Eigenvalue Problems. In: Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations. Springer Series in Computational Mathematics, vol 53. Springer, Singapore. https://doi.org/10.1007/978-981-13-7669-6_10

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