On the Density of Transmission Eigenvalue for the Schrödinger Operator with the Robin Boundary Condition

Li Jie MA, Xiao Chuan XU

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (6) : 959-966.

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Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (6) : 959-966. DOI: 10.12386/A20210064

On the Density of Transmission Eigenvalue for the Schrödinger Operator with the Robin Boundary Condition

  • Li Jie MA, Xiao Chuan XU
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Abstract

In this paper, we study the transmission eigenvalue problem with the Robin boundary condition. Applying the related properties of entire function of exponential type, we show the relationship between the density of eigenvalues and the length of the support interval of the potential function. Meanwhile, we prove that the transmission eigenvalue problem is equivalent to a kind of Sturm-Liouville problem with spectral parameter in the boundary condition.

Key words

transmission eigenvalue / density of zeros / entire function of exponential type / indicator function / Sturm-Liouville problem

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Li Jie MA, Xiao Chuan XU. On the Density of Transmission Eigenvalue for the Schrödinger Operator with the Robin Boundary Condition. Acta Mathematica Sinica, Chinese Series, 2022, 65(6): 959-966 https://doi.org/10.12386/A20210064

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