Convergence of Frame Series: from Hilbert Space to Modulation Space

Analysis Seminar
Wednesday, October 4, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Pu-Ting Yu – Georgia Tech
Benjamin Jaye

It is known that if $\{x_n\}$ is a frame for a separable Hilbert space, then there exist some sequences $\{y_n\}$ such that $x= \sum x_n$, and this sum converges in the norm of H. This equation is called the reconstruction formula of x. In this talk, we will talk about the existence of frames that admit absolutely convergent and unconditionally convergent reconstruction formula. Some characterizations of such frames will also be presented. Finally, we will present an extension of this problem about the unconditional convergence of Gabor expansion in Modulation spaces.