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Using central difference expansions of summations, we study properties of a graduation (smoothing) process in the settings of abelian semigroups with an involution and Dedekind complete vector lattices. We show that a-completely monotone functions, a variant of G. Choquet’s completely monotone functions, are left fixed by graduations satisfying certain positivity conditions. Several numerical and theoretical examples and detailed discussions of various cases are given.

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Completely Monotone Invariance of Smoothing via Central Vector Lattice Differences

  • 会议论文

  • 发表日期：

    2026年

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  • Niyazi Anıl Gezer

摘要

Using central difference expansions of summations, we study properties of a graduation (smoothing) process in the settings of abelian semigroups with an involution and Dedekind complete vector lattices. We show that a-completely monotone functions, a variant of G. Choquet’s completely monotone functions, are left fixed by graduations satisfying certain positivity conditions. Several numerical and theoretical examples and detailed discussions of various cases are given.