lemma A.584 Fourier injectivity in $n$ variables

open in the book · appendices/A-long-proofs.tex:27968 · p. 3072

Rests on

depends_on definition 17.29 Fourier transform; the treatise convention ¶
depends_on equation 17.42 eq:ft-gaussian ¶
depends_on theorem 17.32 Fourier inversion ¶
- depends_on definition 17.29 Fourier transform; the treatise convention ¶ ↺
- depends_on equation 17.42 eq:ft-gaussian ¶ ↺
- proves proof ch:15-fourier-integral-transforms@proof-20 ¶
proves proof app:A-long-proofs@proof-350 ¶

Supports

depends_on theorem A.587 The Gaussian average is a non-zero projector that absorbs the Weyl operators ¶
- depends_on lemma A.590 The Gram matrix is universal ¶
  - depends_on proposition A.591 Any two irreducible Weyl systems are equivalent ¶
- depends_on proposition A.589 Cyclic subspaces and the rank of the average ¶
  - depends_on lemma A.590 The Gram matrix is universal ¶ ↺
  - depends_on proposition A.591 Any two irreducible Weyl systems are equivalent ¶ ↺
- depends_on proposition A.592 The vacuum of the Schrödinger system ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Fourier transform; the treatise convention	declared	appendices/A-long-proofs.tex:27974
`depends_on`	→	eq:ft-gaussian	declared	appendices/A-long-proofs.tex:27974
`depends_on`	→	Fourier inversion	declared	appendices/A-long-proofs.tex:27974
`depends_on`	←	The Gaussian average is a non-zero projector that absorbs the Weyl operators	declared	appendices/A-long-proofs.tex:28082
`proves`	←	app:A-long-proofs@proof-350	declared	appendices/A-long-proofs.tex:27977