内容简介
Aframeinafinite-dimensionalinner-productspaceisacollectionofvectorsspanningthisspace.Inthissense,framesaregeneralizationsoforthonormalbases,whichcanbeusedinmanycaseswhereorthonormalbasescannotbetailoredtofitnaturallyarisingapplications.Thewidearrayofpossibilitiesintroducedbyworkingwithframesratherthanorthonormalbaseshasrevolutionizedmathematicalareassuchaswaveletsandharmonicanalysis.Theadaptabilitytoexistingconditionsallowsframestobeusedinappliedsettingsincludingsignalprocessing,imaging,sampling,andcryptography.Thestudyofframes,particularlyinfinitedimensions,beginswithexactlythetopicsfromanundergraduatelinearalgebracourse.Thismakesthetopicsparticularlyaccessibletoundergraduatestudents,yetthetheorycontainsdeepunsolvedproblems.ThisbookcanbeusedasaresourceforanREUorforatopicscourseaboutframes.Itisalsoasuitabletextbookforasecondlinearalgebracourse,usingframesasathematicexampletodemonstrateandexplorethenewmaterial.Thetheoryofframesisincreasinglybroadwithwidespreadapplications."FramesforUndergraduates"introducesstudentstothisvibrantandimportantareaofmathematics.
作者简介
DeguangHan:UniversityofCentralFlorida,Orlando,FL,KeriKornelson:GrinnellCollege,Grinnell,IA,DavidLarson:TexasA&MUniversity,CollegeStation,TX,EricWeber:IowaStateUniversity,Ames,IA