| Preface |
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vii | |
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1 | (40) |
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6 | (4) |
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1.2 Integration of scalar functions with respect to a vector valued measure |
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10 | (2) |
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1.3 Integration of vector valued functions with respect to a scalar measure |
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12 | (3) |
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1.3.1 The Pettis integral |
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13 | (1) |
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1.3.2 The Bochner integral |
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14 | (1) |
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15 | (9) |
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1.4.1 Injective and projective tensor products |
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17 | (4) |
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1.4.2 Grothendieck's inequality |
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21 | (3) |
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24 | (11) |
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1.5.1 Semivariation in Lp-spaces |
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26 | (6) |
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1.5.2 Semivariation of positive operator valued measures |
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32 | (3) |
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1.6 Bilinear integration after Bartle and Dobrakov |
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35 | (6) |
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2 Decoupled bilinear integration |
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41 | (30) |
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2.1 Bilinear integration in tensor products |
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44 | (9) |
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2.2 Order bounded measures |
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53 | (1) |
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2.3 The bilinear Fubini theorem |
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54 | (5) |
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2.4 Examples of bilinear integrals |
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59 | (12) |
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71 | (30) |
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3.1 Trace class operators |
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72 | (2) |
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3.2 The Hardy-Littlewood maximal operator |
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74 | (1) |
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3.3 The Banach function space of traceable functions |
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75 | (8) |
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3.4 Traceable operators on Banach function spaces |
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83 | (11) |
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91 | (3) |
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3.4.2 Connection with other generalised traces |
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94 | (1) |
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3.5 Hermitian positive operators |
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94 | (7) |
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101 | (22) |
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4.1 Background on probability and discrete processes |
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101 | (10) |
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4.1.1 Conditional probability and expectation |
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104 | (2) |
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4.1.2 Discrete Martingales |
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106 | (3) |
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4.1.3 Discrete stopping times |
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109 | (2) |
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111 | (1) |
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112 | (3) |
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4.3.1 Some properties of Brownian paths |
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114 | (1) |
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4.4 Stochastic integration of vector valued processes |
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115 | (8) |
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123 | (20) |
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5.1 Time-dependent scattering theory |
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123 | (2) |
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5.2 Stationary state scattering theory |
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125 | (3) |
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5.3 Time-dependent scattering theory for bounded Hamiltonians and potentials |
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128 | (3) |
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5.4 Bilinear integrals in scattering theory |
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131 | (7) |
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5.5 Application to the Lippmann-Schwinger equations |
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138 | (5) |
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143 | (28) |
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143 | (5) |
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148 | (2) |
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6.3 Progressive measurability |
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150 | (7) |
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6.4 Operator bilinear integration |
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157 | (10) |
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167 | (4) |
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171 | (20) |
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7.1 Asymptotic estimates for bound states |
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171 | (4) |
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7.2 Lattice traces for positive operators |
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175 | (9) |
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7.3 The CLR inequality for dominated semigroups |
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184 | (7) |
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191 | (38) |
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193 | (9) |
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8.2 Double operator integrals |
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202 | (7) |
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8.3 Traces of double operator integrals |
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209 | (12) |
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8.3.1 Schur multipliers and Grothendieck's inequality |
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212 | (2) |
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8.3.2 Schur multipliers on measure spaces |
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214 | (7) |
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8.4 The spectral shift function |
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221 | (8) |
| Bibliography |
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229 | (8) |
| Index |
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237 | |
Lisainfo e-raamatute kohta