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Gelfand transforms of S O ( 3 ) -invariant Schwartz functions on the free group N 3 , 2

Véronique Fischer, Fulvio Ricci (2009)

Annales de l’institut Fourier

The spectrum of a Gelfand pair ( K N , K ) , where N is a nilpotent group, can be embedded in a Euclidean space. We prove that in general, the Schwartz functions on the spectrum are the Gelfand transforms of Schwartz K -invariant functions on N . We also show the converse in the case of the Gelfand pair ( S O ( 3 ) N 3 , 2 , S O ( 3 ) ) , where N 3 , 2 is the free two-step nilpotent Lie group with three generators. This extends recent results for the Heisenberg group.

General structured bundles

Cabras, Antonella, Kolář, Ivan, Modugno, Marco (1991)

Proceedings of the Winter School "Geometry and Physics"

Summary: [For the entire collection see Zbl 0742.00067.]A general theory of fibre bundles structured by an arbitrary differential-geometric category is presented. It is proved that the structured bundles of finite type coincide with the classical associated bundles.

General theory of Lie derivatives for Lorentz tensors

Lorenzo Fatibene, Mauro Francaviglia (2011)

Communications in Mathematics

We show how the ad hoc prescriptions appearing in 2001 for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier, in a much more general setting encompassing older results of Y. Kosmann about Lie derivatives of spinors.

Generalized Calderón conditions and regular orbit spaces

Hartmut Führ (2010)

Colloquium Mathematicae

The construction of generalized continuous wavelet transforms on locally compact abelian groups A from quasi-regular representations of a semidirect product group G = A ⋊ H acting on L²(A) requires the existence of a square-integrable function whose Plancherel transform satisfies a Calderón-type resolution of the identity. The question then arises under what conditions such square-integrable functions exist. The existing literature on this subject leaves a gap between sufficient and necessary criteria....

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