# Spectral measures and exact domains: NCG companion edition, October 2026

Inherited collection title: *Elliptic Operators & Boundary Problems: Renewed 2026 Course Draft*.

This is a modified version of the earlier course draft *Elliptic Operators & Boundary Problems*.

**Entities responsible for the 2026 modifications:** AN-03 course-writing task and OpenAI Codex.

**Principal author entity of the earlier draft:** AN-03 course-writing task.

**Publisher:** AN-03 local course project.

Copyright © 2026 AN-03 course project contributors.

Copyright © 2026 OpenAI Codex contributors for the NCG companion modifications.

Permission is granted to copy, distribute and modify the 36 revised inherited units under the terms of the GNU Free Documentation License, Version 1.2 only, with no Invariant Sections, no Front-Cover Texts and no Back-Cover Texts. A copy of that license is included in [COPYING](COPYING).

The added CC0 lessons are separate works collected with those units. Their routes are identified in the course metadata. See [Rights and licenses](RIGHTS.md) and [History](HISTORY.md).

## NCG companion modification

**Authors of this companion modification:** GPT-6.1 Sol (OpenAI) and OpenAI Codex. All inherited principal-author and contributor credits above are retained.

**Publisher of this companion edition:** Open Mathematics Courses collection.

The earlier AN-03 mathematical text remains under GFDL 1.2 only. The added zero-space, zero-vector, noninjective-kernel and real-Hilbert-space arguments are new original contributions by the modification entities above, dedicated to CC0 1.0 to the extent rights exist. Their separate source is [CC0 additions](CC0-ADDITIONS.md). The combined modified reading remains GFDL 1.2 only, with no Invariant Sections or Cover Texts; the CC0 dedication does not relicense inherited expression.