Fractional Borg-Levinson Problem with small non-negative potential of small growth

2025/08/09 by Saumyajit Das, Das, Saumyajit, Tuhin Ghosh +1 · 2 citations
Engineering · Mathematics · #35R30 35J10 35K10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical methods in inverse problems #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.2508.06998

openalex publication_date 2025/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we investigate the fractional Borg-Levinson problem, an inverse spectral problem focused on recovering potentials from boundary spectral data. We demonstrate that the potential can, in fact, be uniquely determined by this data. However, for technical reasons, we restrict the fractional exponent to the interval (0.5, 1). Additionally, we assume that at least one of the potentials is small, non-negative, and exhibits mild growth. The smallness condition is made explicit in our calculations and depends only on the domain and the spatial dimension.

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• Anisotropic Calderón problem for a logarithmic Schrödinger operator of order 2+ on closed Riemannian manifolds
• Inverse scattering for the fractional Schrödinger equation

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