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| Beckenbach E., Bellman R. — Inequalities (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge) |
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| Предметный указатель |
 -space 106 107 166—175
Abel, N.H. 32 117 129
Aczel, J. 39 53
Adjoint transformation 79 80
Adjugate matrix 79 80
Aitkin, A.C. 66 90
Alexandroff, P. 80 93
Amir-Moez, A.R. 75 91
Anderson, T.W. 86 96
Andreief, C. 61 88
Arithmetic-geometric mean 10 11
Arithmetic-mean — geometric-mean inequality 3 4
Arithmetic-mean — geometric-mean inequality, refinement of 47
Aronszajn, N. 100 115 129 132 149 165 185
Arrow, K.J. 81 83 84 94 95 159
Artemov, G.A. 146 161
Artin, E. 111
Backward induction 4 5
Banach — Steinhaus theorem 98 118
Banach, S. 94 98 101 107 110 117 118 120 124 125 127 129 139
Beale, E.M.L. 120
Beckenbach's inequality 27
Beckenbach, E.F. 1 16 27 28 50 51 64 89 132 145 146 157 160
Beesack, P.R. 32 53 165 166 178—180 182 185
Bellman, R. 1 2 10 25 30 38 39 48—55 62—67 75—95 105 114—120 126—135 139 141 148 149 154—168 175 182—188
Beltrami, E. 59 132 148 161
Bendat, J. 86 96
Bergman, S. 130
Bergstrom's inequality 67—71
Bergstrom, H. 67—69 71 90
Bernstein's inequality 164 165
Bernstein, S. 109 127 128 164 185
Berwald's inequality 43—44
Berwald, L. 39 43 44 54 101 124 126
Bessel, F.W. 51 99 162
Betti, E. 163
Beurling, A. 55 166 175 186 187
Bieberbach, L. 112 127
Bihari — Langenhop inequality 135 136
Bihari, I. 131 135 136 157
Bing, R.H. 145 160
Birkhoff, G. 31 52 80 82 93 94
Black, H.D. 166 186
Blackwell, D. 52 105 115 126
Blaschke, W. 2 39 53 147 161 177 183 187
Bleuler, K. 146 161
Boas, R.P. 107 127 157 164 165 176 185 187
Bocher, M. 23 51
Bochner, S. 38 53 66 67 100 101 124—126 128 148—150 155 161—163
Bohnenblust, H.F. 52 80 94
Bohr, H. 1 7 50
Bonnesen, T. 29 50 51 104 105
Bonsall, F.F. 132 145 146 160
Borel, E. 94 101 112 115 120 127 130 159
Borg, G. 166 186 187
Bounded variation 108
Branching process 81 93 94
Brauer, A. 80 86 93 95
Brenner, J.L. 90
Brouwer, L.E.J. 93
Brunacci, V. 32
Brunk — Olkin Inequality 49
Brunk, H. D. 48 49 54
Buckner, H. 2 39 54 186
Bullen, P. 53
Buniakowsky's inequality 21—23
Buniakowsky, V. 21—23 39 45 47 98
Burgers, J.M. 154
Burton, L.P. 159
Bush, K.A. 64 89
Calabi, E. 157 163
Canonical representation of quadratic form 68 69
Caplygin, S.A. 131 132 139 140 143 146 157 159 161
Caratheodory, C. 103 112—114 119 127
Carlson's inequality 166 175—177
Carlson, F. 166 175 186
Cartan, H. 100 114 125
Carver, W.B. 119 129
Cassels, J.W.S. 45
Caton, W.B. 166 175 186
Cauchy inequality 2 3 60 61 69 70
Cauchy — Buniakowsky — Schwarz inequality 21—23
Cauchy — Buniakowsky — Schwarz inequality, refinement of 45 46
Cauchy, A.L. 1 2 18 21 45 50 53 60 69 75 90 91 98 102 104 117 158 161
Cauchy-Poincare separation theorem 75 76
Cayley, A. 53
Cebyshev, P.L. 97 109 126 127 187
Cernikov, S.N. 119 129
Cesari, L. 118 129 157
Characteristic equation 71
Characteristic root 55 56 68—86
Characteristic root of largest absolute value 80—83 85
Characteristic root of smallest absolute value 85
Characteristic root with largest real part 83 84
Characteristic vector 82 83
Charnes, A. 119
Chassan, J.B. 45 54
Chern, S. 38 53 90 95
Cherry, I. 162
Chevalley, C.C. 131
Coddington, E. 157 163 179
Colautti, M.P. 165 166 180 181 186
Collatz, L. 81 94 156 163
Complete set of inequalities 98 99 102
Completely positive matrix 96
Compound matrix 79 80
Concave function 6 16—19 29 30 39—44
Concave function of a matrix 75 85
Concavity theorem for matrices 62 63 66—68 74 75
Converse inequality 39—45
Convex function 16—19 29 30 48 50 51 84
Convex function of a matrix 85
Convex function, generalized 132 145 146
Convex set 39 99 103—106 108 119 126
Convex space 103 104
Convexo-concave function 18 51
Cooper, J.L.B. 100 114 125
Corduneanu, C. 118 129
Correlation coefficient 50
Cosine, generalized 2 3 50
Courant, R. 73 91 124 165
Cramer, H. 188
Curtis, P.C.Jr. 145 160
Danskin, J.M. 28 51 80 93
Dantzig, G. 119 120 129
Davis, C.S. 61
de Bruijn, N.G. 61 88
Debreu, G. 81 94
Decision process 85
Dellac, H. 158
Delsarte, J. 132 147 161
Determinant of a matrix 55
Devinatz, A. 114 128
Diananda, P.H. 50
Differential equation 84 135 144
Differential equation, partial 96
Differential equation, partial, of hyperbolic type 85
Differential inequality 17 18 131—134 168—171
Differential operator 131—134 142—144 164—188
Dines, L.L. 119 129
Dinghas, A. 47 54
Dirichlet, P.G.L. 54 160
Discrete inequality 182—185
Dissipative operator 88
Distance function 28
Dobsch, R. 86 96
Doetsch, G. 157 163
Domain of positivity 56 87 88
Dorfman, R. 81 83 95 101 120
Doubly stochastic matrix 31
| Dresher's inequality 28
Dresher, M. 1 28 39 45 51 109 127
du Bois-Reymond, P. 101 126
Dual space 97
Duality 124 125
Duffin, R.J. 86 96 120 130 157 164
Duporcq, E. 158
Dynamic programming 85 95 188
Economy, expanding 83
Eggleston, H.G. 104 126
Ehlers, G. 9 50
Elementary symmetric function 10 11 33—35 78—80
Elliptic equation 148
entropy 55
Erdoes, P. 157
Ergodic theory 55
Esclangon, E. 165
Euclid 23 53 97 103 104
Euler, L. 66 89 124 141 179
Everitt, W.N. 61 88
Expanding economy 83
Fan's inequality 63 74 75
Fan, K. 1 5 32 45 50—56 62 68 71 74—80 84 86 89—96 100 101 110—114 119 120 125—128 166 177 182—186
Farkas, J. 119 129
Favard's inequality 43
Favard, J. 39 43 44 54
Fejer, L. 112 113 127 155
Feller, W. 140 159
Fenchel, W. 29 50—52 104 105
Feynman, R.P. 80 92
Fichera, G. 186
Fischer min-max theorem 72 73
Fischer, E. 56 64 72—75 89 91 112—114 127 130
Folges, M. 50
Ford, L.R.Jr. 120 129
Form, quadratic 3
Forsythe, G.E. 123 131 185 188
Forward induction 4 5
Fourier, J.B.J. 15 25 51 97 98 104 113 125 127 128 178 186 187
Frank — Pick inequality 39—44
Frank, P. 39 43 44 53
Fredholm theory 89
Fredholm, I. 89
Friedrichs, K.O. 101 124 126 131 165 185
Frobenius, G. 56 80 93 94 128
Fuchs, L. 31 32 53
Fulkerson, D.R. 120 129
Function of a matrix 75 85 86
Function of a matrix, concave 75 85
Function of a matrix, monotone 86
Function, concave 6 16—19 29 30 39—44
Function, concave, of a matrix 75 85
Function, convex 16—19 29 30 48 50 51 84
Function, convex, generalized 132 145 146
Function, convex, of a matrix 85
Function, convexo-concave 18 51
Function, distance 28
Function, entropy 55
Function, Green's 40—42 93
Function, polar 28 29
Function, positive 99
Function, positive definite 100 114 115
Function, positive real 86
Function, subharmonic 146
Function, superharmonic 146
Functional equation 6
Furstenberg, H. 157 163
Gabriel, R.M. 166 175 186
Gale, D. 119 120 129 130
Games, theory of 7 83 101 120 121
Gantmacher, V. 56 80 87 93 96
Garner, J.B. 159
Gass, S.I. 120 130
Gauss, C.F. 10 50 187 188
Gelfand, I. 100 114
Gersgorin's inequality 85
Gersgorin, S. 86
Gerstenhaber, M. 85 95
Girding, L. 10 36—38 53 56 66 85 90 95
Gkrding's inequality 37
Glicksberg, I. 25 51 84 91 95 101 120 126
Godemont, R. 100 114 125
Gram, K.P. 51 59 60 88
Gramian 59 60
Graves, L.M. 101 126
Green's function 40—42 93 132—134 141
Green, G. 40 42 93 115 128 129 132 133 141 142 148 149 159 161
Green, J.W. 16 50 156 163
Grenader, U. 100 113 114 128
Greub, W. 45 54 70
Grimshaw, M.E. 76 91
Gronwall, T.H. 131 135 157 158
Gross, O. 25 41 42 51 84 91 95 121 130
Group invariance 67
Guiliano, L. 135 158
Haar — Westphal — Prodi inequality 154
Haar, A. 126 154 162
Hadamard's inequality 64 89
Hadamard, J. 64 89 95 113 158 165 166 185
Hahn, H. 98 101 110 120 124
Halperin, J. 166 172 186
Hamburger, H.L. 76 91
Hardy, G.H. 1 31 32 39 50 51 53 60 129 159 165 166 175 177 179 180 182 186
Harris, T.E. 81 93 94
Hartman, P. 80 93 132 133 144—147 158 160
Hausdorff, F. 128 164
Haviland, E.K. 163
Hayes, W.D. 50
Haynesworth, E.V. 70 86 90 95
Heisenberg, W. 187
Helly, E. 107 110 114 126
Helson, H. 88 97
Herbrand, J. 131
Herglotz, G. 113 114 127
Hermite, C. 53 55—57 64 65 69 85 89—92 119 128
Hermitian matrix 55—57
Hermitian matrix, positive definite 57 64
Hermitian quadratic form 57
Herstein, I.N. 81 94
Hilbert, D. 52 91 98 100 111 114 124 128 165
Hirschman, I.I. 87 96
Hitchcock, H.P. 129
Hoelder's inequality 19—24
Hoelder, O. 1 12 19—21 23 25 27 28 38 39 45 47 51 54 63 98 99 101 104 107 117 167 169 176
Hoffman, A. 62 88 101 120 126
Homogeneity in  21—23
Hopf, E. 163
Hopf, H. 80 93
Hormander, L. 180 188
Horn, A. 75 91
Howard, R. 85 95
Hua, L.K. 65 67 89
Hurwitz, A. 1 8 50 88 117 178 187
Hyers, D. 156 163
Hyperbolic polynomial 36—38 85 90
Hypercomplex number 55
Identity of Lagrange 3
Ince, E.L. 179 187
Induced transformation 79
Induction, backward 4 5
Induction, forward 4 5
Inequality 2
Inequality between arithmetic and geometric means 3 4
Inequality between, refinement of 47
Inequality for characteristic roots 68—80
Inequality for matrix differential equation 136 137
Inequality for matrix minors 63 64
Inequality for minors of a determinant 63
Inequality for polygons 183
Inequality for squares 2
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