Geometric Scattering TheoryThis book is an overview of scattering theory. The author shows how this theory provides a parametrization of the continuous spectrum of an elliptic operator on a complete manifold with uniform structure at infinity. In the first two lectures the author describes the simple and fundamental case of the Laplacian on Euclidean space to introduce the theory's basic framework. In the next three lectures, he outlines various results on Euclidean scattering, and the methods used to prove them. In the last three lectures he extends these ideas to non-Euclidean settings. |
Contents
IV | 1 |
V | 2 |
VI | 4 |
VII | 6 |
VIII | 7 |
IX | 9 |
X | 11 |
XI | 13 |
XLI | 55 |
XLII | 56 |
XLIII | 59 |
XLIV | 62 |
XLV | 65 |
XLVI | 66 |
XLVII | 67 |
XLVIII | 68 |
XII | 15 |
XIII | 18 |
XIV | 19 |
XV | 21 |
XVII | 22 |
XIX | 24 |
XX | 25 |
XXII | 26 |
XXIII | 27 |
XXIV | 30 |
XXV | 33 |
XXVII | 34 |
XXVIII | 36 |
XXIX | 37 |
XXX | 39 |
XXXI | 40 |
XXXII | 42 |
XXXIII | 43 |
XXXIV | 45 |
XXXV | 46 |
XXXVI | 47 |
XXXVII | 48 |
XXXVIII | 51 |
XXXIX | 52 |
XL | 53 |
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Common terms and phrases
analytic continuation asymptotic expansion Atiyah-Patodi-Singer behaviour boundary defining function bounded coefficients cohomology compact manifold compact support consider constant continuous spectrum counting function curvature Diff diffeomorphism differential operators Dirac operator discussed distribution eigenfunctions eigenvalues element elliptic equation Euclidean space exact b-metric extended fact finite follows Footnote Fourier transform Fredholm gives Hodge theory hyperbolic space index theorem infinity integral inverse isomorphism kernel Laplacian Lax-Phillips semigroup Lax-Phillips transform lectures Lemma Lie algebra manifold with boundary manifold with corners meromorphic multiplicity null space obstacle odd dimensions parametrization perturbations polynomial problem properties Proposition pseudodifferential operators Radon transform Reflected geodesics resolvent family result Riemann Ro(A satisfies scattering matrix scattering theory SCTX sense singular smooth solution spectral square-integrable trace class trace formula u₁ unique V₁ vanishes variable vector bundle vector fields Vo(X wave group WF(u X²)u zero Zworski