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1 | (34) |
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Some notions and notations |
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1 | (4) |
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The notion of a domain of positivity |
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5 | (4) |
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The automorphisms of a domain of positivity |
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9 | (3) |
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Norms of a domain of positivity |
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12 | (2) |
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14 | (3) |
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17 | (4) |
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An invariant line element |
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21 | (2) |
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23 | (6) |
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Homogeneous domains of positivity |
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29 | (6) |
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32 | (1) |
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32 | (3) |
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35 | (18) |
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The notion of an ω-domain |
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35 | (3) |
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38 | (2) |
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The geodesics of an ω-domain |
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40 | (5) |
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45 | (3) |
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ω-domains and Jordan algebras |
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48 | (5) |
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50 | (1) |
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51 | (2) |
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53 | (20) |
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53 | (5) |
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The radical of a Jordan algebra |
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58 | (3) |
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The unit element of a Jordan algebra |
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61 | (3) |
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The decomposition theorem |
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64 | (2) |
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66 | (2) |
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Constructions of Jordan algebras |
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68 | (5) |
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71 | (1) |
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71 | (2) |
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Real and Complex Jordan Algebras |
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73 | (20) |
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The quadratic representation |
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73 | (3) |
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76 | (2) |
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A generalization of the fundamental formula |
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78 | (4) |
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82 | (3) |
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The associated Lie algebra |
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85 | (4) |
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89 | (4) |
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90 | (1) |
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91 | (2) |
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93 | (16) |
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Minimal polynomial and eigenvalues |
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93 | (2) |
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95 | (2) |
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The minimal decomposition |
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97 | (2) |
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Applications of the minimal decomposition |
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99 | (3) |
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The eigenvalues of L(u) and P(u) |
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102 | (3) |
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The embedding of real Jordan algebras |
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105 | (4) |
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107 | (1) |
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108 | (1) |
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Jordan Algebras and Omega Domains |
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109 | (18) |
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The ω-domain of a Jordan algebra |
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109 | (4) |
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The Jordan algebra of an ω-domain |
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113 | (2) |
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Jordan algebras with equivalent ω-domains |
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115 | (2) |
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Formally real Jordan algebras |
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117 | (2) |
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Homogeneous domains of positivity |
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119 | (3) |
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Elementary functions on formally real Jordan algebras |
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122 | (2) |
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124 | (3) |
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125 | (1) |
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126 | (1) |
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127 | (30) |
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The half-space of a semisimple Jordan algebra |
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127 | (4) |
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131 | (4) |
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135 | (5) |
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Biholomorphic automorphisms of half-spaces |
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140 | (2) |
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Formally real Jordan algebras |
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142 | (3) |
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The bounded symmetric domain Z |
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145 | (2) |
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Remarks on classification |
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147 | (1) |
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148 | (9) |
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153 | (1) |
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153 | (4) |
| Appendix: The Bergman kernel function |
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157 | (6) |
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157 | (2) |
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2. Domains in complex number space |
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159 | (4) |
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161 | (1) |
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161 | (2) |
| Bibliography |
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163 | (8) |
| Index |
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171 | (4) |
| Biography |
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175 | |
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