4 Introduction
those coefficient s ar e unique . I n fact , i n som e setting s th e linea r
independence an d orthogonalit y restriction s inhibi t th e us e o f ONBs .
Frames can be constructed wit h a wider variety of characteristics, an d
can thu s b e tailore d t o matc h th e need s o f a particula r system .
This boo k give s a n introductio n t o th e stud y o f frame s t o un -
dergraduate student s wh o hav e ha d a cours e i n linea r algebr a an d a
proof-based cours e i n analysis . Th e first chapte r i s a revie w o f som e
concepts fro m linea r algebra , whil e th e secon d chapte r cover s mor e
advanced matri x an d finite-dimensional operato r theory . Th e discus -
sion o f frames begin s i n Chapte r 3 . A student ca n stud y th e chapter s
in order , bu t ma y wis h t o jump righ t int o Chapte r 3 and flip bac k t o
the earlie r chapter s a s needed .
We conside r Chapter s 7 , 8 , an d 9 t o b e advance d topics . Th e
first tw o o f thes e describ e mor e theoretica l result s i n th e theor y o f
frames, whil e th e las t demonstrate s ho w frame s ar e applie d t o actua l
problems i n samplin g theory .
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