Open Research Index

lean-spectral-theory

Ezzeri Esa

Palomar Registrypalomar/PALOMAR-2026-09-01-000004Sep 1, 2026math.FAscore 0

The spectral theorem for possibly unbounded self-adjoint operators on complex Hilbert spaces, formalized through the Cayley transform and real projection-valued measures. The selected spectral theorem constructs a PVM whose scalar measures give the exact finite-second-moment domain and first-moment quadratic form, with measurable-set uniqueness, and is proved equivalent to equality with the unbounded coordinate spectral integral. The selected Stone theorem proves both that strongly continuous one-parameter unitary groups have self-adjoint generators and that every self-adjoint operator…

SourceRepositoryJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/palomar/PALOMAR-2026-09-01-000004
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-01-000004/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-01-000004/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'