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Displaying 21 –
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158
Using the techniques of approximation and factorization of convolution operators we study the problem of irregular sampling of band-limited functions on a locally compact Abelian group . The results of this paper relate to earlier work by Feichtinger and Gröchenig in a similar way as Kluvánek’s work published in 1969 relates to the classical Shannon Sampling Theorem. Generally speaking we claim that reconstruction is possible as long as there is sufficient high sampling density. Moreover, the iterative...
We construct an intrinsic regular surface in the first Heisenberg group equipped wiht its Carnot-Carathéodory metric which has euclidean Hausdorff dimension . Moreover we prove that each intrinsic regular surface in this setting is a -dimensional topological manifold admitting a -Hölder continuous parameterization.
We study finite perimeter sets in step 2 Carnot groups. In this way we extend the classical De Giorgi’s theory, developed in Euclidean spaces by De Giorgi, as well as its generalization, considered by the authors, in Heisenberg groups. A structure theorem for sets of finite perimeter and consequently a divergence theorem are obtained. Full proofs of these results, comments and an exhaustive bibliography can be found in our preprint (2001).
For a riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the riemannian exponential...
For a Riemannian structure on a
semidirect product of Lie groups, the variational problems can be
reduced using the group symmetry.
Choosing the Levi-Civita connection of a positive definite
metric tensor,
instead of any of the canonical connections for the Lie group,
simplifies the reduction of the variations but complicates the
expression for the Lie algebra valued covariant derivatives.
The origin of the discrepancy is in the semidirect product
structure, which implies that the Riemannian
exponential...
The purpose of these survey notes is to give a presentation of a classical theorem of Nomizu [Nom54] that relates the invariant affine connections on reductive homogeneous spaces and nonassociative algebras.
We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new way to regard...
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