We introduce quantum tomography on locally compact Abelian groups $G$. A linear map from the set of states $C^*$-algebra $A(G)$ generated by projective unitary representation $G$ to space characteristic functions is constructed. The dual determining symbols observables derived. Given a function state tomogram consisting probability distributions introduced. provide three examples in which $G={\...

In this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the Fourier transform. As a consequence, we extend the fundamental theorems of Abelian Fourier transform to non-Abelian case.

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

I t has recently been shown by Halmos [l ] that there exists a compact topological group which is algebraically isomorphic to the additive group of the real line, an example being given by the character group of the discrete additive group of the rationals. Exploiting his argument a bit further it is easy to see that the most general such example is the direct sum of N replicas of the one alrea...

In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders. We define a well-behaved derived Hom-complex with values in the derived category of Hausdorff topological abelian groups. Furthermore we introduce a smallness condition for LCA groups and show that such groups have a...

This is a literal reproduction of the 1983 report [55] by Hans G. Feichtinger, with only the obvious typos being corrected, one additional section and minor extra footnotes. Only few symbols have been changed to more standard ones, e.g. for the translation operator (which was L y , following Hans Reiter) has been replaced by T y , and instead of K(G) we write C c (G) now. We hope that by adding...

Let A be a C *-algebra. Let A ⊗ A be the minimal C *-tensor product of A with itself and let M (A ⊗ A) be the multiplier algebra of A ⊗ A. A comultiplication on A is a non-degenerate *-homomorphism ∆ : A → M (A ⊗ A) satisfying the coassociativity law (∆ ⊗ ι)∆ = (ι ⊗ ∆)∆ where ι is the identity map and where ∆ ⊗ ι and ι ⊗ ∆ are the unique extensions to M (A ⊗ A) of the obvious maps on A ⊗ A. We ...

The problem of global optimization of M incoherent phase signals in N complex dimensions is formulated. Then, by using the geometric approach of Landau and Slepian, conditions for optimality are established for N 2, and the optimal signal sets are determined for M 2, 3, 4, 6 and 12. The method is the following: The signals are assumed to be equally probable and to have equal energy, and thus ar...