Linear Systems and Eigenvalue Problems — Problem 29

Definitions and mathematical statement

The supplied record denotes an unspecified kernel by $K$ and an unspecified procedure by $\mathrm{GECP}$. Its mathematical request is:

Prove stronger theoretical bounds for $\mathrm{GECP}$ applied to $K$, exploiting the structure of the kernel $K$.

The record does not define $K$, its domain, its structure, or any matrix associated with it. It also does not define $\mathrm{GECP}$, identify the quantities to be bounded, or give the existing bounds to be strengthened. Consequently, this request cannot be converted into a fully quantified mathematical statement from the supplied evidence. In particular, no class of admissible kernels, hypotheses, boundary conditions, or target inequality is specified. These qualifications remain unresolved.

Short English statement

The problem asks for improved theoretical bounds for the procedure called $\mathrm{GECP}$ applied to a kernel $K$, using its structure. The supplied excerpt omits the definitions and comparison bounds needed to specify a precise mathematical target.

Sources

• Local UnsolvedMath registry: permanent ID $800520$, exact source problem code catalogue entry, title Linear Systems and Eigenvalue Problems — Problem 29. The registry attributes the problem to Amsel, Baumann et al., with proposed year 2026, and labels it open; this is a supplied status label, not an independently verified mathematical assessment.
• Supplied source list: Amsel, Baumann et al., Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop (2026), Problem 29. Supplied URL: https://arxiv.org/abs/2602.05394. The record reports access on 2026-10-16 and extraction by arxiv_latex; these are supplied provenance details, not a claim of independent source consultation.