Abstract
In this chapter we gather together a strategy for investigating wave phenomena in a time domain setting and for developing an associated scattering theory. In the course of this we make more precise many of the statements found in Chapter 1.
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References and Further Reading
R.A. Adams: Sobolev Spaces, Academic Press, New York, 1975.
W.O. Amrein, J.M. Jauch and K.B. Sinha: Scattering Theory in Quantum Mechanics. Lecture Notes and Supplements in Physics, Benjamin, Reading, 1977.
G.R. Baldock and T. Bridgeman: Mathematical Theory of Wave Motion, Ellis Horwood, Chichester, 1981.
D.M. Eidus: The principle of limiting absorption, Math. Sb., 57(99), 1962 and AMS Transl., 47(2), 1965, 157-191.
D.M. Eidus: The principle of limiting amplitude, Uspekhi Mat. Nauk. 24(3), 1969, 91–156 and Russ. Math. Surv. 24(3), 1969, 97-167.
J.A. Goldstein: Semigroups of Linear Operators and Applications, Oxford University Press, Oxford, 1986.
T. Kato: Perturbation Theory for Linear Operators, Springer, New York, 1966.
T. Ikebe: Eigenfunction expansions associated with the Schrodinger Operators and their application to scattering theory, Arch. Rat. Mech. Anal. 5, 1960, 2–33.
P.D. Lax and R.S. Phillips: Scattering Theory, Academic Press, New York, 1967.
R. Leis: Initial Boundary Value Problems of Mathematical Physics, John Wiley & Sons, Chichester, 1986.
A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
D.B. Pearson: Quantum Scattering and Spectral Theory, Academic Press, London, 1988.
M. Reed and B. Simon: Methods of Mathematical Physics, Vols 1-4, Academic Press, New York, 1972-1979.
G.F. Roach: An Introduction to Linear and Nonlinear Scattering Theory, Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 78, Longman, Essex, 1995.
E.J.P. Schmidt: On scattering by time-dependent potentials, Indiana Univ. Math. Jour. 24(10), 1975, 925–934.
H. Tanabe: Evolution Equations, Pitman Monographs and Studies in Mathematics, Vol. 6, Pitman, London, 1979.
C.H. Wilcox: Scattering Theory for the d’Alembert Equation in Exterior Domains, Lecture Notes in Mathematics, No. 442, Springer, Berlin, 1975.
C.H. Wilcox: Scattering states and wave operators in the abstract theory of scattering, Jour. Functional Anal. 12, 1973, 257–274.
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(2008). A Scattering Theory Strategy. In: An Introduction to Echo Analysis. Springer Monographs in Mathematics. Springer, London. https://doi.org/10.1007/978-1-84628-852-4_6
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DOI: https://doi.org/10.1007/978-1-84628-852-4_6
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Print ISBN: 978-1-84628-851-7
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