When do Fourier and Rajchman agree?
Event details
| Date | 20.02.2014 |
| Hour | 10:00 › 11:00 |
| Speaker | Søren Knudby (Københavns Universitet, Denmark) |
| Location | |
| Category | Conferences - Seminars |
Ergodic and Geometric Group Theory Seminar
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? This last algebra is sometimes called the Rajchman algebra.
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 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? This last algebra is sometimes called the Rajchman algebra.
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.
Practical information
- Informed public
- Free
Organizer
- Prof. Nicolas Monod
Contact
- Maxime Gheysens