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<p>In this paper, we study the uniformly exponentially stable quaternionic semigroup and strict Lyapunov exponent via <i>S</i>-spectrum and <i>S</i>-resolvent theory. Some equivalent characterizations of uniformly exponential stability for the strongly continuous quaternionic semigroup are established. Moreover, we construct the quaternionic Green operator functions and establish some equivalent characterizations of quaternionic dichotomous projections. It is crucial to note that we consider operators that do not necessarily commute. Additionally, we study the quaternionic linear operator equations on slice Cauchy domains through establishing some basic properties of <i>n</i>-multiple <i>S</i>-functional calculus of slice hyperholomorphic functions. Besides, the notions of slice sectorially dichotomous and hyperbolic bisectorial operators are introduced and the Yosida approximation and quaternionic semigroup of contractions are considered.</p>

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Quaternionic Linear Operator Equations and Sectorially Dichotomous Operators

  • 期刊论文

  • 发表日期：

    2026年1月4日

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  • Chao Wang,
  • Yiting Li,
  • Jibin Li

摘要

In this paper, we study the uniformly exponentially stable quaternionic semigroup and strict Lyapunov exponent via S-spectrum and S-resolvent theory. Some equivalent characterizations of uniformly exponential stability for the strongly continuous quaternionic semigroup are established. Moreover, we construct the quaternionic Green operator functions and establish some equivalent characterizations of quaternionic dichotomous projections. It is crucial to note that we consider operators that do not necessarily commute. Additionally, we study the quaternionic linear operator equations on slice Cauchy domains through establishing some basic properties of n-multiple S-functional calculus of slice hyperholomorphic functions. Besides, the notions of slice sectorially dichotomous and hyperbolic bisectorial operators are introduced and the Yosida approximation and quaternionic semigroup of contractions are considered.