functional-analysis

This paper extends Topological DeepONets to handle functional measurements on Hausdorff locally convex spaces, replacing point samples with continuous linear functionals and introducing fixed and adaptive measurement systems. The framework is validated on several benchmarks including a non-normable input space, and demonstrates compact, discretization-portable coordinates for operator learning.

本文展示了 GPT-5.5 解决纯泛函分析中精选问题的能力，超越了典型的组合数学与反例任务。

本教程介绍了物理问题中所需的泛函分析概念，涵盖希尔伯特空间、紧算子以及特征函数，面向科学家和工程师。

本文证明了在无限维空间中非线性算子及其导数的首个通用逼近定理，将经典结果扩展到DeepONet和PCA-Net等算子学习架构。