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World Scientific

World Scientific

World

  • Page 2 and 3: GABOR AND WAVELET FRAMES
  • Page 4 and 5: Lecture Notes Series, Institute for
  • Page 6 and 7: CONTENTS Foreword vii Preface ix A
  • Page 8 and 9: FOREWORD The Institute for Mathemat
  • Page 10 and 11: PREFACE The primary interest in Gab
  • Page 12 and 13: Preface xi intermediate frame opera
  • Page 14 and 15: A GUIDED TOUR FROM LINEAR ALGEBRA T
  • Page 16 and 17: From Linear Algebra to the Foundati
  • Page 18 and 19: From Linear Algebra to the Foundati
  • Page 20 and 21: From Linear Algebra to the Foundati
  • Page 22 and 23: From Linear Algebra to the Foundati
  • Page 24 and 25: From Linear Algebra to the Foundati
  • Page 26 and 27: From Linear Algebra to the Foundati
  • Page 28 and 29: From Linear Algebra to the Foundati
  • Page 30 and 31: From Linear Algebra to the Foundati
  • Page 32 and 33: From Linear Algebra to the Foundati
  • Page 34 and 35: From Linear Algebra to the Foundati
  • Page 36 and 37: From Linear Algebra to the Foundati
  • Page 38 and 39: From Linear Algebra to the Foundati
  • Page 40 and 41: From Linear Algebra to the Foundati
  • Page 42 and 43: From Linear Algebra to the Foundati
  • Page 44 and 45: From Linear Algebra to the Foundati
  • Page 46 and 47: From Linear Algebra to the Foundati
  • Page 48 and 49: From Linear Algebra to the Foundati
  • Page 50 and 51: From Linear Algebra to the Foundati
  • Page 52 and 53:

    From Linear Algebra to the Foundati

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    From Linear Algebra to the Foundati

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    From Linear Algebra to the Foundati

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    From Linear Algebra to the Foundati

  • Page 60 and 61:

    From Linear Algebra to the Foundati

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    From Linear Algebra to the Foundati

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    52 A. J. E. M. Janssen where for x,

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    54 A. J. E. M. Janssen monotone con

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    56 A. J. E. M. Janssen algorithms o

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    58 A. J. E. M. Janssen Proof: We ha

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    60 A. J. E. M. Janssen An elementar

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    62 A. J. E. M. Janssen So let c > 0

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    64 A. J. E. M. Janssen From the sec

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    66 A. J. E. M. Janssen As in Subsec

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    68 A. J. E. M. Janssen Hence in cas

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    70 A. J. E. M. Janssen 7. Analysis

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    72 A. J. E. M. Janssen and γk+1 =

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    74 A. J. E. M. Janssen 9. Concludin

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    76 A. J. E. M. Janssen x 0 0 0 A u

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    78 F. Luef In [24] Morita proved th

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    80 F. Luef Janssen’s work on Gabo

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    82 F. Luef of complex numbers of ab

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    84 F. Luef This induces an isomorph

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    86 F. Luef where a1♮Λa2(λ) =

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    88 F. Luef furthermore one has by d

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    90 F. Luef We now define a left act

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    92 F. Luef Let V be a Hilbert A-mod

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    94 F. Luef by Kg,f γ = 〈f, γ〉

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    96 F. Luef compute the symplectic F

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    98 F. Luef The Morita equivalence o

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    100 F. Luef if there are finite pos

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    102 F. Luef functional satisfying

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    104 F. Luef Acknowledgment These in

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    106 F. Luef 38. M. A. Rieffel and A

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    108 P. E. T. Jorgensen matics of wa

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    110 P. E. T. Jorgensen voltages and

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    112 P. E. T. Jorgensen • coherenc

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    114 P. E. T. Jorgensen If only (9)

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    116 P. E. T. Jorgensen A function

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    118 P. E. T. Jorgensen There is a d

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    120 P. E. T. Jorgensen Proposition

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    122 P. E. T. Jorgensen We did not s

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    124 P. E. T. Jorgensen trends in wa

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    126 P. E. T. Jorgensen is solved by

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    128 P. E. T. Jorgensen as noted in

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    130 P. E. T. Jorgensen This process

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    132 P. E. T. Jorgensen Using the sk

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    134 P. E. T. Jorgensen and m0 input

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    136 P. E. T. Jorgensen while mj �

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    138 P. E. T. Jorgensen Further W ˆ

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    140 P. E. T. Jorgensen which is the

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    142 P. E. T. Jorgensen packets. The

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    144 P. E. T. Jorgensen are small, f

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    146 P. E. T. Jorgensen Similarly no

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    148 P. E. T. Jorgensen 2.3.1. The c

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    150 P. E. T. Jorgensen 2.3.2. Gener

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    152 P. E. T. Jorgensen for all f

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    154 P. E. T. Jorgensen The idea of

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    156 P. E. T. Jorgensen holds for al

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    158 P. E. T. Jorgensen from Section

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    160 P. E. T. Jorgensen and the orth

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    162 P. E. T. Jorgensen 12. R. R. Co

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    164 P. E. T. Jorgensen 47. P. E. T.

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    166 P. E. T. Jorgensen 84. V. Strel

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    168 D. R. Larson 1.1. Talks and abs

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    170 D. R. Larson Operator Algebras

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    172 D. R. Larson 1.2.3. Acknowledge

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    174 D. R. Larson operators they wou

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    176 D. R. Larson wandering vector f

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    178 D. R. Larson for each S, T ∈

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    180 D. R. Larson In fact, we specia

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    182 D. R. Larson Proposition 5: Let

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    184 D. R. Larson We have (FTαf)(s)

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    186 D. R. Larson Shannon’s wavele

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    188 D. R. Larson finite dimension.

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    190 D. R. Larson are disjoint and R

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    192 D. R. Larson in actuality the r

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    194 D. R. Larson and let G = A∪B

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    196 D. R. Larson Proof: Write σ =

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    198 D. R. Larson where α(i, j) = (

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    200 D. R. Larson a larger Hilbert s

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    202 D. R. Larson Hence {xn} is not

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    204 D. R. Larson then the strong di

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    206 D. R. Larson {ei : i ∈ I} be

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    208 D. R. Larson Theorem 22: Let EA

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    210 D. R. Larson whose solution cou

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    212 D. R. Larson 7. P. Casazza, D.

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    214 D. R. Larson Processing IX (200

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