Shengda Liu

collaborators

3 papers

math.FA2026

Module-valued ordinary differential equations and structure of solution spaces

Shengda Liu, Yu-Zhe Liu, Keyu Tao

We define and study ordinary differential equations (ODEs) for functions valued in a Banach module $V$ over a finite-dimensional $k$ -algebra $Λ$ by using the tensor of B…

math.CT2025

Normed modules, integral sequences, and integrals with variable upper limits

Miantao Liu, Yu-Zhe Liu, Shengda Liu

This paper provides a new categorification of the Lebesgue integral with variable upper limits by using normed modules over finite-dimensional $k$ -algebras $I^$ and the…

math.RT2025

Normed modules and the categorification of integrations, series expansions, and differentiations

Yu-Zhe Liu, Shengda Liu, Zhaoyong Huang +1

We explore the assignment of norms to $I^$ -modules over a finite-dimensional algebra $I^$ , resulting in the establishment of normed $I^$ -modules. Our primary c…