Välkommen till föreläsningen i seminarieserien i matematik.
Frames generalize the concept of orthonormal bases in Hilbert spaces, they do not require orthogonality and allow redundancy. Still they guarantee perfect and stable reconstruction of all the elements in the Hilbert space (using dual frames), which makes them very useful and valuable for applications. For signal processing, frames of specific structure determined by translations and modulations of some generating function (also called window), play significant role. In this talk, first we will give a brief introduction to frames and dual frames. Then we will focus on Gabor frames and their dual frames, and will present some recent results on characterization of compactly supported dual windows. Through the talk we will also mention some applications of frames.