In shape reconstruction, the celebrated Fourier slice theorem plays an essential role. By virtue of the relation between the Radon transform, the Fourier transform and the 2-dimensional inverse Fourier transform, the shape of an object can be reconstructed from the knowledge of the object’s Radon transform. Unfortunately, a discrete implementation requires the use of interpolation techniques, s...

We propose a definition of a “C-Eberlein” algebra, which is a weak form of a C-bialgebra with a sort of “unitary generator”. Our definition is motivated to ensure that commutative examples arise exactly from semigroups of contractions on a Hilbert space, as extensively studied recently by Spronk and Stokke. The terminology arises as the Eberlein algebra, the uniform closure of the Fourier-Stiel...

0. Introduction. In this paper two commutative, semisimple Banach algebras with involution, viz., A(G) and B(G), (called the Fourier algebra of G and the Fourier-Stieltjes algebra of G, respectively) are defined (as in [5]) for an arbitrary locally compact topological group G. [Note. As algebras A(G) and B(G) are subalgebras of the algebra of bounded continuous functions on G.] The main purpose...