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

2024/05/06 by Pedro Freitas, Freitas, Pedro, Jiř̌í Lipovský +1
Mathematics · #58J52 #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory #Primary: 34L05 #Secondary: 34L40 #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2405.03469

openalex publication_date 2024/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive an expression for the spectral determinant of a second-order elliptic differential operator T defined on the whole real line, in terms of the Wronskians of two particular solutions of the equation 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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