Elements in the Fourier-Stieltjes algebra vanishing at infinity
Speaker: Søren Knudby, UCPH.
The Fourier algebra A(G) and the Fourier-Stieltjes algebra B(G) are function algebras that occur naturally in harmonic analysis of a locally compact group G. Unless G is compact, A(G) is a proper subalgebra of B(G), since functions in A(G) vanish at infinity while B(G) contains the constant functions. Consider the following question: Does the Fourier algebra A(G) coincide with the subalgebra of B(G) consisting of functions vanishing at infinity?
The talk will cover known results concerning this question. It will also include a theorem giving sufficient conditions for the question to have an affirmative answer. As an application of the theorem we are able to give new examples of groups G such that A(G) coincides with the subalgebra of B(G) consisting of functions vanishing at infinity.
The talk will cover known results concerning this question. It will also include a theorem giving sufficient conditions for the question to have an affirmative answer. As an application of the theorem we are able to give new examples of groups G such that A(G) coincides with the subalgebra of B(G) consisting of functions vanishing at infinity.