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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.
This paper demonstrates GPT-5.5's ability to solve selected problems in pure functional analysis, going beyond typical combinatorics and counterexample tasks.
This tutorial introduces functional analysis concepts needed in physical problems, covering Hilbert spaces, compact operators, and eigenfunctions, aimed at scientists and engineers.
This paper proves the first universal approximation theorems for nonlinear operators and their derivatives in infinite-dimensional settings, extending classical results to operator learning architectures like DeepONet and PCA-Net.