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A generalization of a result of Berezin and Gel’fand in the context of Eaton triples is given. The generalization and its proof are Lie-theoretic free and requires some basic knowledge of nonsmooth analysis. The result is then applied to determine the distance between a point and a G-orbit or its convex hull.We also discuss the derivatives of some orbital functions.
We formulate and prove a super analogue of the complex Frobenius theorem of Nirenberg.
Necessary topological conditions are given for the closed CR embedding of a CR manifold into a Stein manifold or into a complex projective space.
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