Prüfer Transformation and Spectral Analysis for a Sturm--Liouville-Type Equation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915697597087744 |
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| author | Bandyopadhyay, Shalmali Çetinkaya, F. Ayça Cuchta, Tom |
| author_facet | Bandyopadhyay, Shalmali Çetinkaya, F. Ayça Cuchta, Tom |
| contents | We study a second-order differential equation involving a quasi-derivative, leading to a non-self-adjoint Sturm--Liouville-type problem with four coefficient functions. To analyze this equation, we develop a generalized Prüfer transformation that expresses solutions in terms of amplitude and phase variables. We further prove the monotonicity of eigenfunction zeros with respect to the spectral parameter and derive upper and lower bounds for the eigenvalues. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_12369 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Prüfer Transformation and Spectral Analysis for a Sturm--Liouville-Type Equation Bandyopadhyay, Shalmali Çetinkaya, F. Ayça Cuchta, Tom Classical Analysis and ODEs Spectral Theory 34L15, 34B24, 34L05 We study a second-order differential equation involving a quasi-derivative, leading to a non-self-adjoint Sturm--Liouville-type problem with four coefficient functions. To analyze this equation, we develop a generalized Prüfer transformation that expresses solutions in terms of amplitude and phase variables. We further prove the monotonicity of eigenfunction zeros with respect to the spectral parameter and derive upper and lower bounds for the eigenvalues. |
| title | Prüfer Transformation and Spectral Analysis for a Sturm--Liouville-Type Equation |
| topic | Classical Analysis and ODEs Spectral Theory 34L15, 34B24, 34L05 |
| url | https://arxiv.org/abs/2508.12369 |