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The article presents an open problem in harmonic analysis concerning the centered maximal operator on the finite cyclic group Z/31Z. It defines the operator Mf(j) as the maximum average of absolute values of a function over intervals of odd length up to 31. The task is to determine the exact L2 operator norm, i.e., the supremum of ||Mf||_2 divided by ||f||_2 for non‑zero functions.
- ▪The problem considers functions f mapping the cyclic group Z/31Z to real numbers.
- ▪The centered maximal operator Mf(j) is defined as the maximum over radii r from 0 to 15 of the average of |f| on the interval j−r to j+r.
- ▪The objective is to find the exact L2 norm of this operator, expressed as the supremum of the ratio ||Mf||_2/||f||_2 for all non‑zero f.
- ▪The question is classified under harmonic analysis and posted as an open problem on TheoremDB.
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Record
| Original publisher | Theoremdb |
| Canonical URL | https://theoremdb.org/ |
| Publication time | Sun, 09 Aug 2026 01:23:36 +0000 |
| Retrieval time | 2026-08-09T03:05:44.926Z |
| Last seen | 2026-08-09T03:05:44.926Z |
| Headline source | Publisher (no WeSearch rewrite) |
| Excerpt source | publisher body |
| Excerpt method | First ~120 words (~800 chars) of extracted publisher body, fair-use limited. |
| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
| Citation coverage | Summary is a WeSearch-generated derivative; primary citation is the original publisher URL. |
| Cluster | rQznSkVQDplO · 1 stories |
| Cluster logic | Grouped by semantic title/content similarity across sources within a rolling window. Same-publisher template collisions are excluded from coverage comparison. |
| Ranking reason | Story pages are not engagement-ranked. Hub feeds use recency, with optional source-diversified chronological ordering (cap consecutive stories per source). No personalized ranking. |
| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
Rights status (four layers)
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| Indexing | May the item be indexed (stored, ranked, made findable)? | Allowed |
| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
| AI summary | May WeSearch generate its own short summary of the article? | Limited |
| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
Basis: Derived from the published RSS/Atom feed. Contact: [email protected]. Reviewed: 2026-07-24.
Opening excerpt (first ~120 words) tap to expand
[#P2692]Sharp L2 norm of the centered maximal operator on C_31OpenFor \(f:\mathbb Z/31\mathbb Z\to\mathbb R\), define \(Mf(j)=\max_{0\leq r\leq15}(2r+1)^{-1}\sum_{k=-r}^{r}|f(j+k)|\). Determine the exact operator norm \(\sup_{f\neq0}\|Mf\|_2/\|f\|_2\).harmonic analysis[#P2692]Open packetOpen in ChatGPT
Excerpt limited to ~120 words for fair-use compliance. The full article is at Theoremdb.
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