Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.19950 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913053697638400 |
|---|---|
| author | Boulton, Lyonell Evans, Connor |
| author_facet | Boulton, Lyonell Evans, Connor |
| contents | We establish a framework to determine the linear completeness of families of non-linear trajectories in Hilbert spaces, which relies on an infinite analytic block Toeplitz operator formulation. By means of this approach, we show the linear completeness in Sobolev spaces of two families of classical functions. One is the moving family of dilated Weierstrass functions. The other is the family of eigenfunctions of the Gross-Pitaevskii equation with trapping potential in an infinite square well. Our results provide a new insight on the formulation of general methods to examine this intriguing concept, bridging classical non-linear analysis and linear approximation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19950 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linear completeness of trajectories in Sobolev spaces and the symmetrised polydisk Boulton, Lyonell Evans, Connor Functional Analysis Spectral Theory 34L10, 34C25, 34B15 We establish a framework to determine the linear completeness of families of non-linear trajectories in Hilbert spaces, which relies on an infinite analytic block Toeplitz operator formulation. By means of this approach, we show the linear completeness in Sobolev spaces of two families of classical functions. One is the moving family of dilated Weierstrass functions. The other is the family of eigenfunctions of the Gross-Pitaevskii equation with trapping potential in an infinite square well. Our results provide a new insight on the formulation of general methods to examine this intriguing concept, bridging classical non-linear analysis and linear approximation theory. |
| title | Linear completeness of trajectories in Sobolev spaces and the symmetrised polydisk |
| topic | Functional Analysis Spectral Theory 34L10, 34C25, 34B15 |
| url | https://arxiv.org/abs/2604.19950 |