Honam Mathematical Journal (호남수학학술지)

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SOME SPECTRAL AND SCATTERING PROPERTIES OF GENERALIZED EIGENPARAMETER DEPENDENT DISCRETE TRANSMISSION STURM-LIOUVILLE EQUATION

  • Received : 2022.12.01
  • Accepted : 2023.03.06
  • Published : 2023.09.14
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Abstract

In this study, we set a boundary value problem (BVP) consisting of a discrete Sturm-Liouville equation with transmission condition and boundary conditions depending on generalized eigenvalue parameter. Discussing the Jost and scattering solutions of this BVP, we present scattering function and find some properties of this function. Furthermore, we obtain resolvent operator, continuous and discrete spectrum of this problem and we give an valuable asymptotic equation to get the properties of eigenvalues. Finally, we give an example to compare our results with other studies.

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Acknowledgement

The authors acknowledge the contributions of other members of committees BD006-02 and BD006, during the development of AS/NZS 1170.2:2021, as well as the many users of the Standard who contributed in the public comment period. The authors also acknowledge the valuable contributions of Dr A.A.S. Pirooz and Dr R. Turner to the analysis of the New Zealand wind data. 

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