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Scattering Theory for dissipative and time-dependent systems has been intensively studied in the last fifteen years. The results in this field, based on various tools and techniques, may be found in many published papers. This monograph presents an approach which can be applied to spaces of both even and odd dimension. The ideas on which the approach is based are connected with the RAGE type theorem, with Enss' decomposition of the phase space and with a time-dependent proof of the existence of the operator W which exploits the decay of the local energy of the perturbed and free systems. Som

Boundary value problems. --- Scattering operator. --- Wave equation.

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This revised edition of a classic book, which established scattering theory as an important and fruitful area of research, reflects the wealth of new results discovered in the intervening years. This new, revised edition should continue to inspire researchers to expand the application of the original ideas proposed by the authors.

Scattering (Mathematics) --- Wave-motion, Theory of. --- Undulatory theory --- Mechanics --- Scattering theory (Mathematics) --- Boundary value problems --- Differential equations, Partial --- Scattering operator --- Equations aux derivees partielles --- Scattering

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Metric spaces --- -Operator theory --- -Scattering operator --- -517.983 --- Operator theory --- Scattering (Physics) --- Functional analysis --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology --- Congresses --- Linear operators. Linear operator equations --- 517.983 Linear operators. Linear operator equations --- -Congresses

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Operator theory --- Scattering (Mathematics) --- Linear systems. --- Operator algebras. --- Hilbert space. --- Dispersion (mathématiques) --- Systèmes linéaires. --- Algèbres d'opérateurs --- Hilbert, Espaces de --- Hilbert space --- Linear systems --- Operator algebras --- Scattering theory (Mathematics) --- Boundary value problems --- Differential equations, Partial --- Scattering operator --- Algebras, Operator --- Topological algebras --- Systems, Linear --- Differential equations, Linear --- System theory --- Banach spaces --- Hyperspace --- Inner product spaces --- Algèbres d'opérateurs. --- Hilbert, Espaces de.

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Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schrödinger equation on the half line with the general selfadjoint boundary condition. The existence, uniqueness, construction, and characterization aspects are treated with mathematical rigor, and physical insight is provided to make the material accessible to mathematicians, physicists, engineers, and applied scientists with an interest in scattering and inverse scattering. The material presented is expected to be useful to beginners as well as experts in the field. The subject matter covered is expected to be interesting to a wide range of researchers including those working in quantum graphs and scattering on graphs. The theory presented is illustrated with various explicit examples to improve the understanding of scattering and inverse scattering problems. The monograph introduces a specific class of input data sets consisting of a potential and a boundary condition and a specific class of scattering data sets consisting of a scattering matrix and bound-state information. The important problem of the characterization is solved by establishing a one-to-one correspondence between the two aforementioned classes. The characterization result is formulated in various equivalent forms, providing insight and allowing a comparison of different techniques used to solve the inverse scattering problem. The past literature treated the type of boundary condition as a part of the scattering data used as input to recover the potential. This monograph provides a proper formulation of the inverse scattering problem where the type of boundary condition is no longer a part of the scattering data set, but rather both the potential and the type of boundary condition are recovered from the scattering data set.

Scattering (Mathematics) --- Scattering theory (Mathematics) --- Boundary value problems --- Differential equations, Partial --- Scattering operator --- Partial differential equations. --- Functional analysis. --- Quantum physics. --- Mathematical physics. --- Partial Differential Equations. --- Functional Analysis. --- Quantum Physics. --- Mathematical Physics. --- Physical mathematics --- Physics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Partial differential equations --- Mathematics