# Gaussian Processes with Sample Paths in Reproducing Kernel Banach Spaces

arXiv: https://arxiv.org/abs/2605.28106 · HTML: https://mlsanity.com/paper/2605.28106/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 16 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 1 of 1)

- [Understanding neural networks with reproducing kernel Banach spaces](https://mlsanity.com/paper/2109.09710/) (2021)

## Abstract (arXiv)

We investigate the connection between Gaussian processes and Gaussian random elements in reproducing kernel Banach spaces. We show that the covariance operator of a weak second-order Radon probability measure on such a space is uniquely determined by a positive definite function. In the Gaussian case, we characterize those positive definite functions that arise from covariance operators in terms of γ-radonifying operators. Building on these results, we extend the classical Driscoll theorem to the Banach space setting.