Analysis seminar

Friday, November 2, 2012 3:30 pm - 3:30 pm EDT

Mehdi Radjabalipour, Iranian Academy of Sciences

“Algebraic frames”

The theory of frames (ordinary, generalized, analytic or algebraic frames) is a setting in which one can study signal processing tools such as: Fourier series, Fourier transform, win-dowed Fourier transform, continuous wavelet transforms, etc. Signals are viewed as elements of a separable complex Hilbert space and the processing can be viewed as application of a rather rich class of linear functionals on these signals. The frames can be divided into two types of analytic or algebraic frames depending on whether the linear functionals involved are bounded (like in the case of Fourier transforms on compact abelian groups) or unbounded (like in the case of locally compact abelian groups). The transformation implementing the signal processing, called the analysis operator, may be a bounded or an unbounded operator on the signal space. The aim of this talk is to study the operator theoretic aspects of the frame theory arising from the analysis operator and its inverse, called the synthesis operator.