The spectral determinant for second order elliptic operators on the real line

Pedro Freitas; Jiří Lipovský

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arXiv · 2405.03469

The spectral determinant for second order elliptic operators on the real line

Pedro Freitas·Jiří Lipovský

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Abstract

We derive an expression for the spectral determinant of a second-order elliptic differential operator $\mathcal{T}$ defined on the whole real line, in terms of the Wronskians of two particular solutions of the equation $\mathcal{T} u=0$. Examples of application of the resulting formula include the explicit calculation of the determinant of harmonic and anharmonic oscillators with an added bounded potential with compact support.

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Pedro Freitas, Jiří Lipovský. 2024-05-06. The spectral determinant for second order elliptic operators on the real line. https://arxiv.org/abs/2405.03469

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