# A Hilbert Space Theory of Generalized Graph Signal Processing

arXiv: https://arxiv.org/abs/1904.11655 · HTML: https://mlsanity.com/paper/1904.11655/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2019.

## Built on by (most cited first, 5 of 5)

- [Time-varying Signals Recovery via Graph Neural Networks](https://mlsanity.com/paper/2302.11313/) (2023)
- [Distributional Signals for Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2304.03507/) (2023)
- [Graph Distribution-valued Signals: A Wasserstein Space Perspective](https://mlsanity.com/paper/2509.25802/) (2025)
- [Spectral Convergence of Complexon Shift Operators](https://mlsanity.com/paper/2309.07169/) (2023)
- [Filter Learning for Subgraphs: Algebras and Performance Risk Bounds](https://mlsanity.com/paper/2607.21263/) (2026)

## Abstract (arXiv)

Graph signal processing (GSP) has become an important tool in many areas such as image processing, networking learning and analysis of social network data. In this paper, we propose a broader framework that not only encompasses traditional GSP as a special case, but also includes a hybrid framework of graph and classical signal processing over a continuous domain. Our framework relies extensively on concepts and tools from functional analysis to generalize traditional GSP to graph signals in a separable Hilbert space with infinite dimensions. We develop a concept analogous to Fourier transform for generalized GSP and the theory of filtering and sampling such signals.