Abstract We consider an operator semigroup arising in the study of an integro-differential equation modeling small transverse vibrations of a viscoelastic pipeline with allowance for Kelvin–Voigt damping. The explicit form of the generator of this semigroup is established, its spectrum is studied, and the norm of its resolvent is estimated. Based on these results, the analyticity of this semigroup is proved with the use of well-known facts from the theory of semigroups.

中文翻译：

---

粘弹性问题中出现算子半群的解析性

摘要 我们考虑了一个算子半群，该算子半群出现在对考虑 Kelvin-Voigt 阻尼的粘弹性管道的小的横向振动进行建模的积分微分方程的研究中。建立了这个半群的生成元的显式，研究了它的谱，估计了它的解算器的范数。基于这些结果，利用半群理论中的众所周知的事实证明了该半群的解析性。