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- W1520582556 abstract "Part I. The Forward Problem: Distinguished solutions Fundamental matrices Fundamental tensors Behavior of fundamental tensors as $|x|rightarrowinfty$ the Functions $Delta_k$ Behavior of fundamental tensors as $zrightarrowinfty$ Behavior of fundamental tensors as $zrightarrow0$ 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 properties 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 $zne0$ Summary of properties of scattering data Part II. The Inverse Problem: Normalized eigenfunctions for odd order inverse data 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^ No. $ Properties of $h^ No. $ Properties of $mu^ No. (x,z)$ and $mu(x,z)$ as $zrightarrowinfty$ and as $xrightarrow-infty$ Proof of the basic inverse theorem The scalar factorization problem for $delta$ The inverse problem at $x=+infty$ and the bijectivity of the map $Lmapsto S(L)=(Z(L),v(L))$ The even order case The second order problem Part III. Applications: Flows Eigenfunction expansions and classical scattering theory Inserting and removing poles Matrix factorization and first order systems Appendix A. Rational approximation Appendix B. Some formulas." @default.
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- W1520582556 date "1988-01-01" @default.
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- W1520582556 title "Direct and Inverse Scattering on the Line" @default.
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