Mathematical foundations of the singularity and eigenmode expansion methods (SEM and EEM)

DOI10.1016/0022-247X(82)90242-6zbMath0486.35065MaRDI QIDQ1164791

Alexander G. Ramm

Publication date: 1982

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

wave propagationscatteringspectral theory of nonselfadjoint operators and pseudo-differential equations

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Wave equation (35L05) Schrödinger operator, Schrödinger equation (35J10)

Related Items (9)

Spectral analysis of integro-differential operators applied in linear antenna modelling ⋮ Modal approximation for time-domain elastic scattering from metamaterial quasiparticles ⋮ Calculating resonances (natural frequencies) and extracting them from transient fields ⋮ Singularities of the inverses of Fredholm operators ⋮ Representation of solutions to Helmholtz’s equation ⋮ Perturbation of resonances ⋮ SOME RESULTS ON INVERSE SCATTERING ⋮ Modal approximation for strictly convex plasmonic resonators in the time domain: the Maxwell's equations ⋮ Spectral properties of some nonselfadjoint operators

Cites Work

• Singularities and energy decay in acoustical scattering
• On the existence of a reduced system of eigenfunctions and generalized eigenfunctions for a nonselfadjoint ordinary differential operator
• Nonspectral singularities of Green's function for the Helmholtz equation in the exterior of an arbitrary convex polygon
• A logarithmic bound on the location of the poles of the scattering matrix
• Growth properties of solutions of the reduced wave equation with a variable coefficient
• Compact Operators with Root Vectors that Span
• High frequency asymptotics of the scattering amplitude for non-convex bodies
• Nonselfadjoint operators in diffraction and scattering
• A variational principle for resonances
• ON THE SHORT WAVE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF STATIONARY PROBLEMS AND THE ASYMPTOTIC BEHAVIOUR ASt→ ∞ OF SOLUTIONS OF NON-STATIONARY PROBLEMS
• Theoretical and practical aspects of singularity and eigenmode expansion methods
• Decaying modes for the wave equation in the exterior of an obstacle
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