Convolution on L
                     p-spaces of a locally compact group

Abtahi, Fatemeh; Nasr-Isfahani, Rasoul; Rejali, Ali

doi:10.2478/s12175-012-0098-6

Cited by 4 publications

(2 citation statements)

References 27 publications

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“…The Heisenberg groups (1) with fixed Lagrangian splitting (G, Γ) form a subclass within all nilquadratic extensions, corresponding to a certain subgroup H 2 G,Γ (P, T ) ≤ H 2 (P, T ) under cohomology. As for all nilquadratic extensions, the Universal Coefficient Theorem induces a short extact sequence (2) 1 G G Ext 1 (P, T ) j G G H 2 (P, T ) q G G Ω 2 (P, T ) G G 0 which splits, albeit not naturally. Here j is the natural embedding of abelian (= symmetric) cocycles while q is the skewing map [γ] → ω with ω(z, w) = γ(z, w)/γ(w, z).…”

Section: Heisenberg Modules and Algebrasmentioning

confidence: 99%

See 1 more Smart Citation

An Algebraic Approach to Fourier Transformation

Rosenkranz,

Landsmann

2020

Preprint

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The notion of Fourier transformation is described from an algebraic perspective that lends itself to applications in Symbolic Computation. We build the algebraic structures on the basis of a given Heisenberg group (in the general sense of nilquadratic groups enjoying a splitting property); this includes in particular the whole gamut of Pontryagin duality. The free objects in the corresponding categories are determined, and various examples are given. As a first step towards Symbolic Computation, we study two constructive examples in some detail-the Gaussians (with and without polynomial factors) and the hyperbolic secant algebra.

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Section: Heisenberg Modules and Algebrasmentioning

confidence: 99%

“…In a natural-though less conventional-extension, we shall speak of a Heisenberg algebra if the module is additionally equipped with a compatible multiplication. 2 Definition 18. Let β : Γ × G → T be a duality, and let K be a ring with torus action ε T .…”

Section: //mentioning

confidence: 99%