| Title: |
A survey of sampling discretization of integral and uniform norms |
| Authors: |
Dai, F.; Kosov, E.; Temlyakov, V. |
| Publication Year: |
2026 |
| Collection: |
ArXiv.org (Cornell University Library) |
| Subject Terms: |
Numerical Analysis; Functional Analysis |
| Description: |
This paper surveys recent developments in the sampling discretization of integral and uniform norms for functions in general finite-dimensional spaces. These results generalize the classical Marcinkiewicz-Zygmund inequalities for trigonometric and algebraic polynomials, which play a crucial role in Fourier analysis, interpolation, and approximation theory. We focus on the problem in the broad context of finite-dimensional subspaces, where norms defined by general probability measures are approximated by their discrete counterparts. The primary emphasis is on results closely related to the authors' recent research. A key objective is to highlight the main ideas and techniques that form the foundation of the proofs in this area. This survey serves as a complement to three recently published survey papers on sampling discretization \cite{DPTT, KKLT, LMT}. |
| Document Type: |
text |
| Language: |
unknown |
| Relation: |
http://arxiv.org/abs/2603.02459 |
| Availability: |
http://arxiv.org/abs/2603.02459 |
| Accession Number: |
edsbas.3C1D425B |
| Database: |
BASE |