HARMONIC ANALYSIS ON RIEMANNIAN SYMMETRIC SPACES OF NEGATIVE CURVATURE AND SCATTERING THEORY

1976 ◽  
Vol 10 (3) ◽  
pp. 535-563 ◽  
Author(s):  
M A Semenov-Tjan-Šanskiĭ
Keyword(s):  
Harmonic Analysis ◽  
Scattering Theory ◽  
Negative Curvature ◽  
Symmetric Spaces ◽  
Riemannian Symmetric Spaces

Scattering on Riemannian Symmetric Spaces and Huygens Principle

2018 ◽  
Vol 30 (08) ◽  
pp. 1840015
Author(s):  
Michael Semenov-Tian-Shansky
Keyword(s):  
Wave Equation ◽  
Scattering Theory ◽  
Symmetric Spaces ◽  
Evolution System ◽  
Semisimple Lie Groups ◽  
Curved Space ◽  
Zero Curvature ◽  
Famous Paper ◽  
Huygens Principle ◽  
Riemannian Symmetric Spaces

The famous paper by L. D. Faddeev and B. S. Pavlov (1972) on automorphic wave equation explored a highly romantic link between Scattering Theory (in the sense of Lax and Phillips) and Riemann hypothesis. An attempt to generalize this approach to general semisimple Lie groups leads to an interesting evolution system with multidimensional time explored by the author in 1976. In the present paper, we compare this system with a simpler one defined for zero curvature symmetric spaces and show that the Huygens principle for this system in the curved space holds if and only if it holds in the zero curvature limit.

Scattering theory for symmetric spaces of noncompact type

1993 ◽  
Vol 72 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Ralph S. Phillips ◽  
Mehrdad M. Shahshahani
Keyword(s):  
Scattering Theory ◽  
Symmetric Spaces ◽  
Noncompact Type

scholarly journals Wave propagation on Riemannian symmetric spaces

1992 ◽  
Vol 107 (2) ◽  
pp. 270-278 ◽  
Author(s):  
G. 'Olafsson ◽  
H. Schlichtkrull
Keyword(s):  
Wave Propagation ◽  
Symmetric Spaces ◽  
Riemannian Symmetric Spaces
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