definition 9.54 Sturm–Liouville differential operator

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• depends_on definition 16.75 Rayleigh quotient ¶
  • depends_on definition A.462 The weighted space and the energy space ¶
    • depends_on lemma A.463 Poincaré inequality; $B_{K}$ is an inner product ¶
      • depends_on lemma A.464 $H_{E}$ is a Hilbert space ¶
      • depends_on lemma A.466 The homogeneous Dirichlet problem is trivial ¶
        • depends_on definition A.467 Green function of the shifted problem ¶
        • depends_on theorem A.469 The Green operator inverts $L_{K}$ ¶
      • depends_on theorem A.469 The Green operator inverts $L_{K}$ ¶ ↺
  • depends_on proposition 28.38 Rayleigh's bound on the lowest frequency ¶
  • depends_on theorem A.461 Completeness in the weighted and in the energy norm ¶
• depends_on definition 9.105 Modified Bessel functions ¶
  • depends_on proposition 9.106 The modified series and what it does not do ¶
• depends_on lemma 9.56 Lagrange identity ¶
  • depends_on lemma A.442 The Wronskian of the accessory equation is constant ¶
    • depends_on definition A.467 Green function of the shifted problem ¶ ↺
    • depends_on theorem A.443 Sturm separation theorem ¶
  • depends_on theorem 9.57 Orthogonality of Sturm–Liouville eigenfunctions ¶
    • depends_on phenomenon 28.53 Chladni's figures ¶
    • depends_on phenomenon 28.45 The harmonic series of a stretched string ¶
    • depends_on theorem 9.119 Orthogonality at fixed order ¶
      • depends_on theorem 9.122 Normalisation and orthonormality ¶
    • depends_on theorem 9.98 Orthogonality of the Bessel functions ¶
      • depends_on proposition 9.100 Fourier–Bessel coefficients ¶
    • depends_on theorem 9.127 Orthogonality ¶
      • depends_on proposition 9.128 Hermite series ¶
    • depends_on theorem 9.133 Orthonormality ¶
      • depends_on proposition 9.134 Laguerre series ¶
    • depends_on theorem 9.111 Orthogonality of the Legendre polynomials ¶
      • depends_on proposition 9.115 Legendre series ¶
      • depends_on theorem 9.119 Orthogonality at fixed order ¶ ↺