On Weyl Function Of Singular Sturm-Liouville Operator With Transmission Conditions

This paper focuses on the Weyl function of Sturm-Liouville (S-L) operator with one singular endpoint and transmission conditions. Limit circle, limit point are defined in the new space which is generated by the new inner product. We give the definition of Weyl function, discuss the nature of the Weyl function and give properties of weyl solutions by Weyl function, and we prove that the Weyl solutions belong to L2(â… ). Finally, similar to the classic case, we investigate the spectral function of S-L operator with one singular endpoint and transmission conditions, discuss the relationship between Weyl function and spectral function.