Wave propagation on Riemannian symmetric spaces
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
Wave propagation on Riemannian symmetric spaces. / 'Olafsson, G.; Schlichtkrull, H.
I: Journal of Functional Analysis, Bind 107, Nr. 2, 01.08.1992, s. 270-278.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Wave propagation on Riemannian symmetric spaces
AU - 'Olafsson, G.
AU - Schlichtkrull, H.
PY - 1992/8/1
Y1 - 1992/8/1
N2 - Let X = G K be a Riemannian symmetric space of the noncompact type and let LX be the Laplace-Beltrami operator on X. We consider on X × R a differential equation of the type LXu = P(∂t)u, where P(∂t) is a second order differential operator in t ε{lunate} R. Using the Radon transform on X we relate Huygens' principle for the solutions u to this equation, to the corresponding question for the solutions v to the equation LAv = (P(∂t) + R)v on a maximal flat subspace A, where R is a certain explicit constant. In particular we conclude that Huygens' principle holds for solutions to the (modified) wave equation on X obtained by letting P(∂t) = ∂t2 - R, when X is odd-dimensional and G has one conjugacy class of Cartan subgroups.
AB - Let X = G K be a Riemannian symmetric space of the noncompact type and let LX be the Laplace-Beltrami operator on X. We consider on X × R a differential equation of the type LXu = P(∂t)u, where P(∂t) is a second order differential operator in t ε{lunate} R. Using the Radon transform on X we relate Huygens' principle for the solutions u to this equation, to the corresponding question for the solutions v to the equation LAv = (P(∂t) + R)v on a maximal flat subspace A, where R is a certain explicit constant. In particular we conclude that Huygens' principle holds for solutions to the (modified) wave equation on X obtained by letting P(∂t) = ∂t2 - R, when X is odd-dimensional and G has one conjugacy class of Cartan subgroups.
UR - http://www.scopus.com/inward/record.url?scp=38249009303&partnerID=8YFLogxK
U2 - 10.1016/0022-1236(92)90107-T
DO - 10.1016/0022-1236(92)90107-T
M3 - Journal article
AN - SCOPUS:38249009303
VL - 107
SP - 270
EP - 278
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -
ID: 304298616