definition A.438 Momentum variable and the accessory system

open in the book · appendices/A-long-proofs.tex:21517 · p. 3007

ground object -- no derivation owed

Rests on

depends_on equation 16.49 eq:calcvar-jacobi ¶
depends_on equation 9.3 eq:slt-ode-system ¶

Supports

depends_on lemma A.439 Existence, uniqueness, and the structure of the zeros ¶
- 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 lemma A.468 The kernel is well defined, symmetric and Lipschitz ¶
      - depends_on theorem A.470 $T$ is compact ¶
    - 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 ¶
- depends_on theorem A.441 Continuous dependence on the data and on the initial point ¶
  - depends_on corollary A.445 Displacing the initial point ¶

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`	→	eq:calcvar-jacobi	declared	appendices/A-long-proofs.tex:21535
`depends_on`	→	eq:slt-ode-system	declared	appendices/A-long-proofs.tex:21535
`depends_on`	←	Existence, uniqueness, and the structure of the zeros	declared	appendices/A-long-proofs.tex:21551