AI 中文总结
本文针对时间分数阶偏微分方程，详细构造参数依赖的伪微分算子族的参基，研究渐近展开项与参数的依赖关系及光滑余项，还给出向量值分布拉普拉斯变换的相关结果。
AI 中文摘要
我们详细证明了如何构造参数依赖的伪微分算子族的参基，该算子族出现在时间分数阶偏微分方程的分析中。特别地，我们精确研究了对应渐近展开项对参数的依赖关系，以及光滑余项的情况。此外，我们还提供了关于向量值分布拉普拉斯变换的一些结果，该变换也出现在时间分数阶偏微分方程的分析中。
英文摘要
We prove in detail how to construct the parametrix of a parameter-dependent family of pseudodifferential operators, appearing in the analysis of time-fractional partial differential equations. In particular, we perform a precise study of the dependence from the parameter of the corresponding asymptotic expansion terms, as well as of the smoothing remainders. Moreover, we provide some results about the Laplace transform of vector-valued distributions, also appearing in the analysis of time-fractional partial differential equations.
Comments18 pages. Materials originally included in the first version of arXiv:2511.04885
