# General reproducing properties in RKHS with application to derivative and integral operators

arXiv: https://arxiv.org/abs/2503.15922 · HTML: https://mlsanity.com/paper/2503.15922/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 15 references that are in the map.
- First posted on arXiv 20 Mar 2025.

## Builds on (most cited first, 3 of 3)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Targeted Separation and Convergence with Kernel Discrepancies](https://mlsanity.com/paper/2209.12835/) (2022)
- [Minimum Kernel Discrepancy Estimators](https://mlsanity.com/paper/2210.16357/) (2022)

## Built on by (most cited first, 1 of 1)

- [Multifidelity Gaussian process regression for solving nonlinear partial differential equations](https://mlsanity.com/paper/2605.10383/) (2026)

## Abstract (arXiv)

In this paper, we consider the reproducing property in Reproducing Kernel Hilbert Spaces (RKHS). We establish a reproducing property for the closure of the class of combinations of composition operators under minimal conditions. This allows to revisit the sufficient conditions for the reproducing property to hold for the derivative operator, as well as for the existence of the mean embedding function. These results provide a framework of application of the representer theorem for regularized learning algorithms that involve data for function values, gradients, or any other operator from the considered class.