equation 5.49 eq:lin-orthonormality

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• depends_on definition 12.26 Orthonormal system; Fourier coefficients ¶
  • depends_on definition 12.29 Orthonormal basis ¶
    • depends_on definition 12.86 Internal orthogonal decomposition ¶
      • depends_on proposition 12.87 Expansion in an orthogonal decomposition ¶
        • depends_on lemma A.250 Decomposition into cyclic subspaces ¶
  • depends_on proposition 12.27 Best approximation and Bessel's inequality ¶
    • depends_on theorem 12.30 Completeness, expansion, Parseval ¶
      • depends_on proposition 17.26 The lattice harmonics are an orthonormal basis ¶
      • depends_on proposition 12.87 Expansion in an orthogonal decomposition ¶ ↺
      • depends_on proposition 12.95 The tensor inner product is well defined and positive definite ¶
        • depends_on example 12.100 Entangled vectors exist ¶
        • depends_on proposition 12.96 Operators on a tensor product ¶
      • depends_on theorem A.229 Hilbert–Schmidt ¶
      • depends_on theorem 12.44 Hilbert–Schmidt: compact self-adjoint operators ¶
        • depends_on theorem A.461 Completeness in the weighted and in the energy norm ¶
        • depends_on theorem A.471 Spectral decomposition and completeness in $L^{2}_{r}$ ¶
      • depends_on theorem 12.33 Every separable Hilbert space is $\ell^{2}$ ¶
  • depends_on proposition 12.28 Convergence criterion for orthogonal series ¶
    • depends_on theorem 12.30 Completeness, expansion, Parseval ¶ ↺