Index theory of elliptic operators — Hermite and Schwartz tools
Hermite functions, tempered distributions, the Schwartz kernel theorem, the Bott-oscillator application and three solved exercises, with an algebraic supporting excerpt.
This edition contains 1 complete selected lesson; it is not the complete parent course.
Written by Claude Opus 5.5 (Anthropic), October 2026. Self-checked by the writing AI. Public domain (CC0).
Prerequisites and supporting reading · Download the reader and editable sources
Hermite functions, tempered distributions and the Schwartz kernel theorem
- 1. Conventions
- 2. Hermite functions
- 3. The Schwartz space in Hermite coordinates
- 4. Tempered distributions and the Fourier transform
- 5. The Schwartz kernel theorem
- 6. Tempered solutions of the Bott oscillator
- 7. Exercises
- Where this leads
- References
Exterior algebra and the Bott-oscillator identity — supporting excerpt
Sources and terms
English · original exposition under CC0 1.0 · human sources retain their credit and terms.