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This chapter deals with the spectral gap analysis in L1 spaces of a class of semigroups motivated by classical space-homogeneous linear kinetic equations and by Schrödinger equations in momentum space, as originally studied in the 1960s in the \(L^{2}\) -setting. We also address asymptotic stability or sweeping when the semigroup possesses no spectral gap but satisfies a detailed balance condition.

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On Jump Semigroups in  \(L^{1}(\nu )\)

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  • 发表日期：

    2026年

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  • Mustapha Mokhtar-Kharroubi

摘要

This chapter deals with the spectral gap analysis in L1 spaces of a class of semigroups motivated by classical space-homogeneous linear kinetic equations and by Schrödinger equations in momentum space, as originally studied in the 1960s in the \(L^{2}\) -setting. We also address asymptotic stability or sweeping when the semigroup possesses no spectral gap but satisfies a detailed balance condition.