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

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.

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Uncertainty principles for the Schrödinger equation on Riemannian symmetric spaces of the noncompact type

Annales de l’institut Fourier ◽

10.5802/aif.2710 ◽

2012 ◽

Vol 62 (3) ◽

pp. 859-886 ◽

Cited By ~ 5

Author(s):

Angela Pasquale ◽

Maddala Sundari

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Symmetric Spaces ◽

Uncertainty Principles ◽

Noncompact Type ◽

Riemannian Symmetric Spaces

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A Reconstruction Theorem for Riemannian Symmetric Spaces of Noncompact Type

Journal of Fourier Analysis and Applications ◽

10.1007/s00041-009-9090-0 ◽

2009 ◽

Vol 15 (6) ◽

pp. 839-856 ◽

Cited By ~ 2

Author(s):

Matthew B. Stenzel

Keyword(s):

Symmetric Spaces ◽

Noncompact Type ◽

Reconstruction Theorem ◽

Riemannian Symmetric Spaces

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HYPERSURFACES IN NONCOMPACT COMPLEX GRASSMANNIANS OF RANK TWO

International Journal of Mathematics ◽

10.1142/s0129167x12501030 ◽

2012 ◽

Vol 23 (10) ◽

pp. 1250103 ◽

Cited By ~ 20

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.

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The $\Theta$-spherical transform and its inversion

MATHEMATICA SCANDINAVICA ◽

10.7146/math.scand.a-14459 ◽

2004 ◽

Vol 95 (2) ◽

pp. 265 ◽

Cited By ~ 1

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.

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COMPLEX CROWNS OF SYMMETRIC SPACES

International Journal of Mathematics ◽

10.1142/s0129167x05003156 ◽

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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