Index
adjoint, 43 , 44 , 45 , 49 , 6 4
analysis operator , 94 , 100, 104,
111, 151, 159, 217
Banach space , 184
bandlimited subspace , 239 , 25 2
basis, 10, 11-17 , 62 , 88 , 145, 157
Hamel, 11
orthonormal, see also
orthonormal basi s
transition matrix , 2 3
Beurling density , 26 2
bijection, 17
bounded operator , 7 4
Cauchy-Schwarz, 29 , 39 , 23 9
Chebyshev algorithm , 11 9
co-isometry, 4 8
commutant, 219
complete space , 3 0
compression, 141, 144
condition number , 108, 119
conjugate gradien t algorithm , 120
coordinate vector , 2 1
determinant, 27 7
diagram vector , 124, 129, 131
dilation, 141
dimension, 15, 24 , 52 , 9 5
direct su m - orthogonal , 17, 34 , 35 ,
36, 5 5
direct su m - vecto r space , 16, 39 ,
62, 265 , 27 4
discrete Fourie r transform , 143,
237, 238 , 243 , 25 1
disjoint frames , 168, 169
dual frame , 100, 156-163, 175
alternate, 157
canonical, 157, 161, 162, 169,
214
Parseval, 175, 177
dual space , 4 2
eigenspace, 61, 62 , 63 , 65 , 77-8 1
eigenvalue, 60 , 62-67 , 77 , 79 , 107,
187, 214, 26 5
eigenvector, 61, 62-67 , 79 , 26 5
ellipsoid, 189
ellipsoidal tigh t frame , 189, 195,
196
embedding, 51, 5 2
equivalent frames , 126
PRR-equivalence, 127
equivalent norms , 184
evaluation functional , 23 5
Fourier basis , 237 , 25 1
Fourier inversio n formula , 25 6
Fourier transform , 25 5
Fourier Uncertaint y Principle , 239 ,
249
293
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