lemma A.442 The Wronskian of the accessory equation is constant

open in the book · appendices/A-long-proofs.tex:21739 · p. 3009

Rests on

depends_on lemma A.439 Existence, uniqueness, and the structure of the zeros ¶
- depends_on corollary 9.9 Linear equations: existence on the whole interval ¶
  - depends_on definition 9.2 Linear equation; homogeneity ¶
    - depends_on definition 9.1 Ordinary differential equation ¶
  - depends_on remark 9.3 Normal form and first-order systems ¶
  - depends_on theorem 9.8 Picard–Lindelöf ¶
    - depends_on definition 9.4 Lipschitz condition ¶
    - depends_on equation 9.3 eq:slt-ode-system ¶
    - depends_on lemma 9.6 Weierstrass $M$-test; uniform limits are continuous ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on proposition 7.47 Comparison; absolute convergence ¶
      - proves proof ch:07-odes-sturm-liouville@proof-1 ¶
    - proves proof ch:07-odes-sturm-liouville@proof-2 ¶
  - proves proof ch:07-odes-sturm-liouville@proof-3 ¶
- depends_on definition A.438 Momentum variable and the accessory system ¶
  - depends_on equation 16.49 eq:calcvar-jacobi ¶
  - depends_on equation 9.3 eq:slt-ode-system ¶ ↺
- proves proof app:A-long-proofs@proof-261 ¶
depends_on lemma 9.56 Lagrange identity ¶
- depends_on definition 9.54 Sturm–Liouville differential operator ¶
- proves proof ch:07-odes-sturm-liouville@proof-28 ¶
proves proof app:A-long-proofs@proof-264 ¶

Supports

depends_on definition A.467 Green function of the shifted problem ¶
- depends_on lemma A.468 The kernel is well defined, symmetric and Lipschitz ¶
  - depends_on theorem A.470 $T$ is compact ¶
    - depends_on theorem A.471 Spectral decomposition and completeness in $L^{2}_{r}$ ¶
      - depends_on lemma A.472 The pairing identity ¶
- depends_on theorem A.469 The Green operator inverts $L_{K}$ ¶
  - depends_on lemma A.472 The pairing identity ¶ ↺
  - depends_on theorem A.471 Spectral decomposition and completeness in $L^{2}_{r}$ ¶ ↺
depends_on theorem A.443 Sturm separation theorem ¶

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`	→	Existence, uniqueness, and the structure of the zeros	declared	appendices/A-long-proofs.tex:21748
`depends_on`	→	Lagrange identity	declared	appendices/A-long-proofs.tex:21748
`depends_on`	←	Green function of the shifted problem	declared	appendices/A-long-proofs.tex:22970
`depends_on`	←	Sturm separation theorem	declared	appendices/A-long-proofs.tex:21785
`proves`	←	app:A-long-proofs@proof-264	declared	appendices/A-long-proofs.tex:21751