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A. Demonvelberthier, D. Manda (1995)
Spectral and Scattering-Theory for Wave-Propagation in Perturbed Stratified MediaJournal of Mathematical Analysis and Applications, 191
S. Agmon (1975)
Spectral properties of Schrödinger operators and scattering theoryAnnali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 2
S. Debievre, D. Pravica (1992)
Spectral analysis for optical fibres and stratifled fluids II: Absence of Eigenvalues ∗Communications in Partial Differential Equations, 17
D. Eidus (1986)
The limiting absorption and amplitude principles for the diffraction problem with two unbounded mediaCommunications in Mathematical Physics, 107
Yoshimi Saito (1974)
The principle of limiting absorption for the non-selfadjoint Schrödinger operator in R²Osaka Journal of Mathematics, 11
Jl Cj, Jl (1974)
The Principle of Limiting Absorption for the Non
C. Wilcox (1984)
Sound Propagation in Stratified Fluids
Teruo Ikebe, Yoshimi Saito (1972)
Limiting Absorption Method and Absolute Continuity for the Schrodinger Operator (位相解析の物理数学への応用)
(1994)
On radiation conditions for acoustic propagators in perturbed 35 stratified fluids
Yoshimi Saito (1989)
A REMARK ON THE LIMITING ABSORPTION PRINCIPLE FOR THE REDUCED WAVE EQUATION WITH TWO UNBOUNDED MEDIAPacific Journal of Mathematics, 136
R. Weder (1988)
Absence of eigenvalues of the acoustic propagator in deformed wave guidesRocky Mountain Journal of Mathematics, 18
(1989)
Acoustic waves in perturbed stratified fluids: a spectral theory
R. Weder (1990)
Spectral and Scattering Theory for Wave Propagation in Perturbed Stratified Media
G. Roach, Bo Zhang (1992)
On Sommerfeld radiation conditions for the diffraction problem with two unbounded mediaProceedings of the Royal Society of Edinburgh: Section A Mathematics, 121
S. Debievre, D. Pravica (1991)
Spectral Analysis for Optical Fibres and Stratified Fluids I: The Limiting Absorption PrincipleJournal of Functional Analysis, 98
Yoshimi Saito (1971)
The Principle of Limiting Absorption for Second-order Differential Equations with Operator-valued Coefficients*Publications of The Research Institute for Mathematical Sciences, 7
(1995)
Saitö: The reduced wave eguation in layered materials
Abstract. Consider the differential operator //= -- () 1 in the Hubert space X = L2(RN', ()), where is the Laplacian in RN, and () is a positive simple function on RN. Let S be the surface on which is discontinuous (the separating surface). So far the stratified media in which the separating surface S consists of parallel surfaces have been vigorously studied. Also the case where S has a cone shape has been discussed. In this work we shall deal with a new type of discontinuity which we call cylindrical discontinuity. Under this condition we shall use the limiting absorption method to prove that H is absolute continuous. Our method is based on a priori estimates of radiation condition term. 1991 Mathematics Subject Classification: 35P05. §1. Introduction Consider the differential expression (1.1) = -()- 1 . Here is the Laplacian in RN with N > 2, and () is a positive function on RN given by (1.2) (*) where 1( 2 > , 2, and ,, 7 = 1,2, are open sets of RN such that This work was supported by Deutsche Forschungsgemeinschaft through SFB 359. W. J ger, . Saito | being the closure of {.
Forum Mathematicum – de Gruyter
Published: Jan 1, 1997
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