Measurable transformations on compact groups

Measurable Transformations

Semiparametric estimation of rigid transformations on compact Lie groups

To cite this version: Bigot, Jérémie and Loubes, Jean-Michel and Vimond, Myriam Semiparametric estimation of shifts on compact Lie groups. (2008) In: 2nd MICCAI Workshop on Mathematical Foundations of Computational Anatomy, 6 September 2008 6 September 2008 (New York, United States). Open Archive Toulouse Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulo...

Spaces of Measurable Transformations

By a space we shall mean a measurable space, i.e. an abstract set together with a <r-ring of subsets, called measurable sets, whose union is the whole space. The structure of a space will be the <r-ring of its measurable subsets. A measurable transformation from one space to another is a mapping such that the inverse image of every measurable set is measurable. Let X and F be spaces, F a set of...

On component extensions locally compact abelian groups

Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...

Bracket Products on Locally Compact Abelian Groups

We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).