Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X2220170401Normalized tight vs. general frames in sampling problems1141254333510.22034/aot.1611-1063ENTomaž KoširFaculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, SloveniaMatjaž OmladičJournal Article20161124We present a new approach to sampling theory using the operator theory framework. We use a replacement operator and replace general frames of the sampling and reconstruction subspaces by normalized tight frames. The replacement can be done in a numerically stable and efficient way. The approach enables us to unify the standard consistent reconstruction results with the results for quasiconsistent reconstruction. Our approach naturally generalizes to consistent and quasiconsistent reconstructions from several samples. Not only we can handle sampling problems in a more efficient way, we also answer questions that seem to be open so far.http://www.aot-math.org/article_43335_a0eb80054183c1d231c2f48925a39cca.pdf