19 citations · 33 across the 16 of their papers we have counts for
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Holomorphic horospherical transform on non-compactly causal spaces
Simon Gindikin, Bernhard Kroetz, Gestur Olafsson
We develop integral geometry for non-compactly causal symmetric spaces. We define a complex horospherical transform and, for some cases, identify it with a Cauchy type integral.
Complex horospherical transform on real sphere
Simon Gindikin
We define a new integral transform on the real sphere which is invariant relative to the orthogonal group and similar to the horospherical Radon transform for the hyperbolic space.…
Horospherical Cauchy-Radon transform on compact symmetric spaces
Simon Gindikin
Harmonic analysis on noncompact Riemannian symmetric spaces is in a sense equivalent to the theory of the horospherical transform. There are no horospheres on compact symmetric spa…
Horospherical model for holomorphic discrete series and horospherical Cauchy transform
Simon Gindikin, Bernhard Kroetz, Gestur Olafsson
We define a complex horospherical transform for affine symmetric spaces of Hermitian type and show that it has no kernel on the holomorphic discrete series.
Holomorphic H-spherical distribution vectors in principal series representations
Simon Gindikin, Bernhard Kroetz, Gestur Olafsson
Let G/H be a semisimple symmetric space. The main tool to embed a principal series representation of G into L^2(G/H) are the H-invariant distribution vectors. If G/H is a non-compa…
A remark on Schubert cells and duality of orbits on flag manifolds
Simon Gindikin, Toshihiko Matsuki
It is known that the closure of an arbitrary K_c-orbit on a flag manifold is expressed as a product of a closed K_c-orbit and a Schubert cell ([M2], [Sp]). We already applied this…