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Hermitizable, Isospectral Matrices or Differential Operators

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Dirichlet Forms and Related Topics (IWDFRT 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 394))

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Abstract

This paper reports the study on Hermitizable problem for complex matrix or second order differential operator. That is the existence and construction of a positive measure such that the operator becomes Hermitian on the space of complex square-integrable functions with respect to the measure. In which case, the spectrum are real, and the corresponding isospectral matrix/differntial operators are described. The problems have a deep connection to computational mathematics, stochastics, and quantum mechanics.

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Acknowledgements

This study is supported by the National Natural Science Foundation of China  (Project No.: 12090011), National key R &D plan  (No. 2020YFA0712900). Supported by the “double first class” construction project of the Ministry of education (Beijing Normal University) and the advantageous discipline construction project of Jiangsu Universities. It is an honor to the author to contribute the paper to the Festschrift in honor of Masatoshi Fukushima’s Beiju. Thank are also given to an unknown referee for the corrections of typos of an earlier version of the paper.

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Authors and Affiliations

  1. Research Institute of Mathematical Science, Jiangsu Normal University, Shanghai Lu 101, Tongshan Xinqu, Xuzhou, 221116, China

    Mu-Fa Chen

  2. Key Laboratory of Mathematics and Complex System, School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Mu-Fa Chen

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  1. Mu-Fa Chen
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Correspondence to Mu-Fa Chen .

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Editors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, USA

    Zhen-Qing Chen

  2. Department of Mathematics, Kansai University, Osaka, Japan

    Masayoshi Takeda

  3. Department of Mathematics, Kansai University, Osaka, Japan

    Toshihiro Uemura

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Chen, MF. (2022). Hermitizable, Isospectral Matrices or Differential Operators. In: Chen, ZQ., Takeda, M., Uemura, T. (eds) Dirichlet Forms and Related Topics. IWDFRT 2022. Springer Proceedings in Mathematics & Statistics, vol 394. Springer, Singapore. https://doi.org/10.1007/978-981-19-4672-1_3

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