Frames for Undergraduates

Aframeinafinite-dimensionalinner-productspaceisacollectionofvectorsspanningthisspace.Inthissense,framesaregeneralizationsoforthonormalbases,whichcanbeusedinmanycaseswhereorthonormalbasescannotbetailoredtofitnaturallyarisingapplications.Thewidearrayofpossibilitiesintroducedbyworkingwithframesratherthanorthonormalbaseshasrevolutionizedmathematicalareassuchaswaveletsandharmonicanalysis.Theadaptabilitytoexistingconditionsallowsframestobeusedinappliedsettingsincludingsignalprocessing,imaging,sampling,andcryptography.Thestudyofframes,particularlyinfinitedimensions,beginswithexactlythetopicsfromanundergraduatelinearalgebracourse.Thismakesthetopicsparticularlyaccessibletoundergraduatestudents,yetthetheorycontainsdeepunsolvedproblems.ThisbookcanbeusedasaresourceforanREUorforatopicscourseaboutframes.Itisalsoasuitabletextbookforasecondlinearalgebracourse,usingframesasathematicexampletodemonstrateandexplorethenewmaterial.Thetheoryofframesisincreasinglybroadwithwidespreadapplications."FramesforUndergraduates"introducesstudentstothisvibrantandimportantareaofmathematics.