Completeness of the wave operators for perturbations of uniformly propagative systems

DOI10.1016/0022-1236(71)90028-0zbMath0223.47007OpenAlexW2013188618MaRDI QIDQ2548069

John R. Schulenberger, Calvin H. Wilcox

Publication date: 1971

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(71)90028-0

Mathematics Subject Classification ID

Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Perturbation theory of linear operators (47A55)

Related Items

Completeness of the wave operators for scattering problems of classical physics, Unnamed Item, The scattering theory of lax and phillips and wave propagation problems of classical physics^†‡, A compactness result for vector fields with divergence and curl in L^q(ω) involving mixed boundary conditions, A two Hilbert space scattering theorem, The scattering of classical waves from inhomogeneous media, On partition of energy for uniformly propagative systems, The Schrödinger formalism of electromagnetism and other classical waves -- how to make quantum-wave analogies rigorous, Coerciveness inequalities for nonelliptic systems of partial differential equations, A Rellich uniqueness theorem for steady-state wave propagation in inhomogeneous anisotropic media, The limiting absorption principle and spectral theory for steady-state wave propagation in inhomogeneous anisotropic media, A coerciveness inequality for a class of nonelliptic operators of constant deficit, The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system. I, Scattering states and wave operators in the abstract theory of scattering, Eigenfunction expansions and scattering theory for wave propagation problems of classical physics, On conservative boundary conditions for operators of constant deficit: the Maxwell operator, Spectral and scattering theory of one-dimensional coupled photonic crystals, The conjugate operator method for strongly singular operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On finite-dimensional perturbations of self-adjoint operators
• Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory
• Wave operators and asymptotic solutions of wave propagation problems of classical physics
• Steady-state wave propagation in homogeneous anisotropic media
• Scattering theory with two Hilbert spaces
• Uniqueness theorems for a class of wave propagation problems
• Transient wave propagation in homogeneous anisotropic media
• Spectral and scattering theory for symmetric hyperbolic systems in an exterior domain
• Coerciveness inequalities for nonelliptic systems of partial differential equations
• The Green's matrix for steady state wave propagation in a class of inhomogeneous anisotropic media
• On the existence and the unitary property of the scattering operator
• Perturbation of continuous spectra by Trace class operators
• A Sufficient Condition for an Integral Operator to Have a Trace.
• On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems
• Theory of Simple Scattering and Eigenfunction Expansions
• Scattering theory
• Symmetric hyperbolic linear differential equations