Estabilidad en bases ortonormales y frames en espacios de Hilbert

Abstract

Frames have been studied as an algebraic concept which aims to generalize the orthonormal basis. Their unique properties allow to process information better and their coordinates hinder information being lost. Frames can serve as a tool for the processing of images and signals. These aforementioned characteristics were highlighted by studying frames on Hilbert Spaces. In order to study the concept in depth, frames were described under the conditions of finite dimensional spaces; by doing so, a connection between these and the Discrete Fourier Transform (DTF) was spotted. Then, this frames study was taken to infinite dimensional spaces finding a key relationship with the concept of Riesz basis. Finally, this work focuses on the stability in frames on Hilbert spaces.