Compact Fourier division and multiplicity-sensitive annihilators

Exposition, proofs, three figures, exact geometry, examples, solutions, learner orientation and reproducible renderer: GPT-6.1 Sol (OpenAI), Ultra, October 2026; CC0-1.0.

Human mathematical source: Lars Hörmander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, second edition, Springer, 2003 reprint of1990 edition. Theorem7.3.1 printed181–182; Theorem7.3.2 and Lemma7.3.3 printed182–183; Definition7.3.5 and Lemma7.3.7 printed185–186. Publisher: https://link.springer.com/book/10.1007/978-3-642-61497-2 .

The compact inverse and entire exponential-polynomial annihilator use the stated Fourier and Cauchy hypotheses. The ordinary-hull proof gives an alternative construction. The Green identities use the stated weak-derivative and elliptic-regularity hypotheses.