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The structure of jump semigroups in Lebesgue spaces \(L^{1}(E,\nu )\) significantly simplifies when the measure space is countable, such as \(\mathbb {N}\) equipped with the counting measure. In this chapter, we address peripheral spectral analysis and time asymptotics for Kolmogorov differential equations on sequence spaces \(l^{1}(\mathbb {N} ),\) equipped with (weighted) counting measures. We also address the hilbertian spectral gap analysis of Dirichlet forms associated with symmetric weighted graphs, with killing term, defined over abstract countable measure spaces.

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Jump Semigroups on Countable State Spaces

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  • 发表日期：

    2026年

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  • Mustapha Mokhtar-Kharroubi

摘要

The structure of jump semigroups in Lebesgue spaces \(L^{1}(E,\nu )\) significantly simplifies when the measure space is countable, such as \(\mathbb {N}\) equipped with the counting measure. In this chapter, we address peripheral spectral analysis and time asymptotics for Kolmogorov differential equations on sequence spaces \(l^{1}(\mathbb {N} ),\) equipped with (weighted) counting measures. We also address the hilbertian spectral gap analysis of Dirichlet forms associated with symmetric weighted graphs, with killing term, defined over abstract countable measure spaces.