# 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.

Original text: CC0.

## 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 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 reading, including the earlier AN-03 mathematical text, is dedicated to CC0 1.0.