proof ch:10-hilbert-spaces@proof-16

open in the book · parts/02-mathematical-methods/10-hilbert-spaces.tex:765

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proof : ch:10-hilbert-spaces@proof-16prooftheorem 12.30: Completeness, expansion, Parseval12.30corollary 12.19: Double complement; the density criterion12.19proposition 12.27: Best approximation and Bessel's inequality12.27proposition 12.28: Convergence criterion for orthogonal series12.28proposition 17.26: The lattice harmonics are an orthonormal basis17.26proposition 12.87: Expansion in an orthogonal decomposition12.87proposition 12.95: The tensor inner product is well defined and positive definite12.95theorem A.229: Hilbert–SchmidtA.229theorem 12.44: Hilbert–Schmidt: compact self-adjoint operators12.44theorem 12.33: Every separable Hilbert space is \ell^212.33

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