A Basic Inequality for Scattering Theory on Riemannian Symmetric Spaces of the Noncompact Type

1991 ◽  
Vol 113 (3) ◽  
pp. 391 ◽  
Author(s):  
Jean-Philippe Anker
Keyword(s):  
Scattering Theory ◽  
Symmetric Spaces ◽  
Noncompact Type ◽  
Basic Inequality ◽  
Riemannian Symmetric Spaces

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

Theorems of Ingham and Chernoff on Riemannian symmetric spaces of noncompact type

2020 ◽  
Vol 279 (11) ◽  
pp. 108760
Author(s):  
Mithun Bhowmik ◽  
Sanjoy Pusti ◽  
Swagato K. Ray
Keyword(s):  
Symmetric Spaces ◽  
Noncompact Type ◽  
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.

HYPERSURFACES IN NONCOMPACT COMPLEX GRASSMANNIANS OF RANK TWO

2012 ◽  
Vol 23 (10) ◽  
pp. 1250103 ◽  
Author(s):  
JÜRGEN BERNDT ◽  
YOUNG JIN SUH
Keyword(s):  
Geometric Structure ◽  
Symmetric Spaces ◽  
Second Fundamental Form ◽  
Kähler Structure ◽  
Noncompact Type ◽  
The Second Fundamental Form ◽  
Special Cases ◽  
Rank One ◽  
Higher Rank ◽  
Riemannian Symmetric Spaces

Consider a Riemannian manifold N equipped with an additional geometric structure, such as a Kähler structure or a quaternionic Kähler structure, and a hypersurface M in N. The geometric structure induces a decomposition of the tangent bundle TM of M into subbundles. A natural problem is to classify all hypersurfaces in N for which the second fundamental form of M preserves these subbundles. This problem is reasonably well understood for Riemannian symmetric spaces of rank one, but not for higher rank symmetric spaces. A general treatment of this problem for higher rank symmetric spaces is out of reach at present, and therefore it is desirable to understand this problem better in a few special cases. Due to some conceptual differences between symmetric spaces of compact type and of noncompact type it appears that one needs to consider these two cases separately. In this paper we investigate this problem for the rank two symmetric space SU 2, m/S(U2Um) of noncompact type.

scholarly journals The $\Theta$-spherical transform and its inversion

2004 ◽  
Vol 95 (2) ◽  
pp. 265 ◽  
Author(s):  
Angela Pasquale
Keyword(s):  
Laplace Transform ◽  
Compact Support ◽  
Inversion Formula ◽  
Symmetric Spaces ◽  
Expansion Formula ◽  
Noncompact Type ◽  
Riemannian Symmetric Spaces

The $\Theta$-spherical transform is defined as a simultaneous generalization of the Harish-Chandra's spherical transform on Riemannian symmetric spaces of noncompact type and of the spherical Laplace transform on noncompactly causal symmetric spaces as defined by Faraut, Hilgert and Ólafsson. An extension of Ólafsson's expansion formula allows us to deduce an inversion formula for the $\Theta$-spherical transform on the space of $W_\Theta$-invariant $C^\infty$ functions with compact support.

COMPLEX CROWNS OF SYMMETRIC SPACES

2005 ◽  
Vol 16 (08) ◽  
pp. 889-902
Author(s):  
RÓBERT SZŐKE
Keyword(s):  
Symmetric Spaces ◽  
Complex Structure ◽  
Noncompact Type ◽  
Riemannian Symmetric Spaces

The notion of complex crowns is extended from Riemannian symmetric spaces of noncompact type to general symmetric spaces using the adapted complex structure construction.

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