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Transcendence and the Expression of the Spectral Series of a Class of Higher Order Differential Operators

Author

Listed:
  • Bing Xie

    (School of Mathematics and Statistics, Shandong University, Weihai 264209, China)

  • Jing Li

    (School of Mathematics and Statistics, Shandong University, Weihai 264209, China)

  • Jiangang Qi

    (School of Mathematics and Statistics, Shandong University, Weihai 264209, China)

Abstract

In this paper, a relationship between the spectral zeta series of a class of higher order self-adjoint differential operators on the unit circle and the integral of Green functions is established by Mercer’s Theorem. Furthermore, the explicit expression and the transcendental nature of the spectral series are obtained by the integral representation. Finally, several applications in physics about differential operators’ spectral theory, yellow some further works, and the transcendental nature of some zeta series are listed.

Suggested Citation

  • Bing Xie & Jing Li & Jiangang Qi, 2023. "Transcendence and the Expression of the Spectral Series of a Class of Higher Order Differential Operators," Mathematics, MDPI, vol. 11(3), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:636-:d:1047786
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