The Forward Problem: Distinguished solutions / Part I: |
Fundamental matrices Fundamental tensors |
Behavior of fundamental tensors as $|x|\rightarrow\infty$; the Functions $\Delta_k$ |
Behavior of fundamental tensors as $z\rightarrow\infty$ |
Behavior of fundamental tensors as $z\rightarrow0$ |
Construction of fundamental matrices |
Global properties of fundamental matrices; the transition matrix $\delta$ |
Symmetries of fundamental matrices |
The Green's function for $L$ |
Generic operators and scattering data |
Algebraic properties of scattering data |
Analytic roperties of scattering data |
Scattering data for $\tilde m$; determination of $\tilde v$ from $v$ |
Scattering data for $L^\ast$ Generic selfadjoint operators and scattering data |
The Green's function revisited |
Genericity at $z=0$ Genericity at $z\ne0$ |
Summary of properties of scattering data |
The Inverse Problem: Normalized eigenfunctions for odd order inverse data / Part II: |
The vanishing lemma |
The Cauchy operator Equations for the inverse problem |
Factorization near $z=0$ and property (20.6) |
Reduction to a Fredholm equation Existence of $h^\#$ |
Properties of $h^\#$ Properties of $\mu^\#(x,z)$ and $\mu(x,z)$ as $z\rightarrow\infty$ and as $x\rightarrow-\infty$ |
Proof of the basic inverse theorem |
The scalar factorization problem for $\delta$ |
The inverse problem at $x=+\infty$ and the bijectivity of the map $L\mapsto S(L)=(Z(L),v(L))$ The even order case The second order problem |
Applications: Flows / Part III: |
Eigenfunction expansions and classical scattering theory |
Inserting and removing poles |
Matrix factorization and first order systems |
Rational approximation / Appendix A: |
Some formulas / Appendix B: |
The Forward Problem: Distinguished solutions / Part I: |
Fundamental matrices Fundamental tensors |
Behavior of fundamental tensors as $|x|\rightarrow\infty$; the Functions $\Delta_k$ |
Behavior of fundamental tensors as $z\rightarrow\infty$ |
Behavior of fundamental tensors as $z\rightarrow0$ |
Construction of fundamental matrices |