In this paper, we investigate the resolvent operator of the singular q-Sturm-Liouville problem defined as
−(1/q)Dq⁻¹[Dqy(x)]+[r(x)-λ]y(x)=0−(1/q)Dq⁻¹Dqy(x)+r(x)y(x)=λy(x),
with the boundary condition y(0,λ)cosβ+Dq⁻¹y(0,λ)sinβ=0y(0,λ)cosβ+Dq⁻¹y(0,λ)sinβ=0,
where λ∈Cλ∈C, $r$ is a real function defined on $[0,∞)$, continuous at zero and r∈Lq,loc¹(0,∞)r∈Lq,loc¹(0,∞). We give an integral representation for the resolvent operator and investigate some properties of this operator. Furthermore, we obtain a formula for the Titchmarsh-Weyl function of the singular $q$-Sturm-Liouville problem.
q-Sturm-Liouville operator spectral function resolvent operator Titchmarsh-Weyl function
Birincil Dil | İngilizce |
---|---|
Konular | Uygulamalı Matematik |
Bölüm | Research Article |
Yazarlar | |
Yayımlanma Tarihi | 31 Aralık 2021 |
Gönderilme Tarihi | 22 Ocak 2021 |
Kabul Tarihi | 3 Nisan 2021 |
Yayımlandığı Sayı | Yıl 2021 Cilt: 70 Sayı: 2 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
This work is licensed under a Creative Commons Attribution 4.0 International License.