Simultaneous Approximation on Affine Subspaces

Diophantine Exponents of Affine Subspaces: the Simultaneous Approximation Case

We apply nondivergence estimates for flows on homogeneous spaces to compute Diophantine exponents of affine subspaces of Rn and their nondegenerate submanifolds.

On Covering Approximation Subspaces

Let (U ′; C′) be a subspace of a covering approximation space (U ; C) and X ⊂ U ′. In this paper, we show that C′(X) = C(X)⋂ U ′ and B′(X) ⊂ B(X) ⋂ U ′. Also, C(X) = C′(X)⋂ C(U ′) iff (U ; C) has Property Multiplication. Furthermore, some connections between outer (resp. inner) definable subsets in (U ; C) and outer (resp. inner) definable subsets in (U ′; C′) are established. These results ans...

A Note on the Structure of Affine Subspaces of

This paper investigates the structure of general affine subspaces of ( )  L . For a d × d expansive matrix A, it shows that every affine subspace can be decomposed as an orthogonal sum of spaces each of which is generated by dilating some shift invariant space in this affine subspace, and every non-zero and non-reducing affine subspace is the orthogonal direct sum of a reducing subspace and a ...

A Bollobás-type theorem for affine subspaces

Barycentric Subspaces and Affine Spans in Manifolds

This paper addresses the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. Current methods like Principal Geodesic Analysis (PGA) and Geodesic PCA (GPCA) minimize the distance to a ”Geodesic subspace”. This allows to build sequences of nested subspaces which are consistent with a forward component analysis approach. However, these methods cannot be adapted to a backw...