Parameter Holes in Bessel Wave Packet Systems
Manuscript 24 October 2026 · Online 24 October 2026
Abstract
We prove that a Bessel wave packet system generated by a nonzero L2 function, with an arbitrary discrete parameter set in the affine Weyl-Heisenberg group, has a parameter set missing a left translate of every compact set. Hence all lower densities in the Czaja-Kutyniok-Speegle convention vanish and the lower Beurling dimension is zero. The proof uses explicit left Folner averaging of translated counting measures and the known divergent continuous coefficient integral. No product structure or extra generator regularity is assumed. The necessary nonzero-generator qualification and the degenerate zero exception are explicit. This is an unrefereed preprint with an originating-researcher self-audit, not independent review, formal verification or a certified priority claim. The manuscript was developed with OpenAI Codex assistance. Source dataset record: OWR-720-006 (ulamai/UnsolvedMath v1.6.0). The manuscript discloses OpenAI Codex assistance.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Complete proof
- Categories
- math.FA · math.CA
- Manuscript
- 24 October 2026
- Online release
- 24 October 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “Parameter Holes in Bessel Wave Packet Systems,” EulerSolve Research Papers, OWR-720-006, 2026. https://doi.org/10.5281/zenodo.23621541.
BibTeX
@misc{ferudun2026parameterholes,
author = {Ferudun, Alper},
title = {Parameter Holes in Bessel Wave Packet Systems},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/owr-720-006/},
doi = {10.5281/zenodo.23621541},
note = {OWR-720-006; unrefereed preprint}
}