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| Beckenbach E., Bellman R. — Inequalities (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge) |
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| Предметный указатель |
inequality operator 131
Inequality with alternating signs 47 48
Inequality, additive from multiplicative 77
Inequality, complete set of 98 99 102
Inequality, converse 39—45
Inequality, differential 17 18 131—144 168—171
Inequality, discrete 182—185
Inequality, integral 21—23
Inequality, linear 119—121
Inequality, mean-value 23
Inequality, multiplicative from additive 77 78
Inequality, new from old 46 47
Inequality, partial differential 146 163
Inequality, triangle 20 24 55
Information theory 55
Ingham — Siegel integral 65
Ingham, A.E. 55 56 65 66 89 90
Inner product 3 45—47 57 60 61 87 98
Inone, M. 146 160
Input-output matrix 83 84 95
Integral equation, Fredholm theory of 89
Integral inequality 21—23
Integral, Kellogg kernel in 96
Integration over groups 8
Interaction theorem 98
Ising problem 94 128
Jackson, L.K. 146 160
Jacobi, K.G. 62 80 143
Jacobson, N. 61 88
Jacobsthal, E. 11 51
Jensen's inequality 18
Jensen, J.L.W.V. 18 51
Jentzsch, R. 93
John, F. 152 162
Kac, M. 113 128 133 148 158
Kaczmarz, S. 123 131
Kalaba, R. 30 52 55 163
Kantorovich, L.V. 54
Karamata's inequality 30—32
Karamata, J. 1 30 31 52 88
Karlin, S. 56 80 81 87 92 94 97 100 101 109 111 120 125 127 133 137
Kellogg kernel 96
Kellogg, O.D. 87 96
Kemeny, J.G. 94
Kernel, reproducing 115 128 129 149
Kerner, E.H. 80 92
Kesten, H. 157 163
Kjellberg, B. 166 175 176 186
Klein, F. 53
Klimko, E.Y. 146 161
Kneser, H. 39 54
Kober, H. 47 54
Koecher, M. 56 87 97
Kolmogoroff, A. 61 88 165 182 185
Konyushkov, A.A. 187
Koranyi, A. 115 128
Korn, A. 165
Kraus, F. 86 96
Krein, M.G. 56 80 81 87 93 94 96 185 188
Kronecker product 79
Kronecker, L. 79 92
Kuhn, H. 120 130
L'Hospital, G.F.A. 16
Lagrange identity 3 60
Lagrange multiplier 5
Lagrange — Beltrami theorem 59
Lagrange, J.L. 1 3 5 59 60 67 179
Landau, E. 100 101 112 114 116 118 127—129 165 185
Landau, H.J. 178 187
Lane, A.M. 86 96
Langenhop, C.E. 131 135 136 157
Langer, R. 163
LaSalle, J.P. 158
Lax, P.D. 38 56 85 95 101 110 124 126 131 135 158 162
Le marquis de Laplace, P.S. 66 125 148 161 163
Lebesgue, H. 118
Lees, M. 158
Lefschetz, S. 157 158 163
Lehman, S. 120 130
Leipnik, R. 55
Lemke, C.E. 119
Leontieff, W.W. 81 83 94 159
Levin, V.I. 166 176 186
Levinson, N. 157 163 179
Levitan, B. 128 132 147 161
Liapunov, A. 115 129 158
Lidskii, V.B. 75 91
Liiroth, J. 51
Linear inequalities 119—121
Linear programming 94 95 101 120
Liouville, J. 140 142 148 159 162 166 178 179
Lipschitz, R. 90
Littlewood, J.E. 1 31 32 39 50 51 53 60 129 165 166 177 179 180 182 186
Loewner, C. 56 86 96 157 159
Lojasiewicz, S. 187
Loomis, L.H. 114 121 128 130
Lopes, L. 1 33 35 53 79
Lorch, E.R. 29 50 52 90 92 110
Lorentz space 38
Lorentz, G.G. 1 32 53
Lorentz, H.A. 38 53
Lowdenslager, D. 88 97
Lyapunov, A. 92 166 188
Mac Duffee, C.C. 61 79 88 92
Maclaurin, C. 11 50
Madansky, A. 45 54
Mahler, K. 1 29 51 97
Mairhuber, J.C. 87 97
Majorization 7 8
Mallows, C.L. 100 103 105 116 126
Mandelbrojt, S. 165 185
Maradudin, A. 113 128
Marcienkiewicz, J. 30 52
Marcus — Lopes Inequality 33—35
Marcus, M. 1 33 35 53 64 79 89 92
Markoff matrix 93
Markoff, A.A. 80 85 87 88 92 93 139 158 165 185
Markovian decision process 85 87
Marshall, A. 88 97
Masani, P. 88 97
Massera, J.L. 118 129 139 159
Mathias, M. 100 114 125
Matrix exponential 137
Matrix modular function 90
Matrix, adjugate 79 80
Matrix, completely positive 96
Matrix, complex 55 57
Matrix, complex, with positive definite real part 62
Matrix, compound 79 80
Matrix, doubly stochastic 31
Matrix, hermitian 55—-57
Matrix, hermitian, positive definite 57 64
Matrix, input-output 83 84 94 138
Matrix, Markoff 80 93
Matrix, nonnegative 93
Matrix, nonnegative definite 57
Matrix, nonnegative, principal minors of 58
Matrix, orthogonal 93
Matrix, positive 56 80
Matrix, positive definite 3 55—64 87
Matrix, positive indefinite 57
Matrix, positive, as sum of squares 58 59
Matrix, positive, principal minors of 57—59
Matrix, stability 88
Matrix, stochastic 80
Matrix, symmetric 57
Matrix, Toeplitz 113 128
Matrix, trace of 66 70 87
Matrix, unitary 93
Maximum principle 132 133
| McGregor, J.L. 56 79 80 87 92 97 133
McNabb, A. 154 162
Mean of order t 16
Mean, arithmetic-geometric 10 11
Mean-value inequality 23
Mean-value theorem 144 146 147 149 150 161
Menger, K. 55
Mewborn, A.C. 81 94
Min-max theorem of Fischer 72 73
Min-max theorem of von Neumann 83 120 121
Minkowski's inequality 19—27
Minkowski's inequality for products 26
Minkowski, H. 1 12 19—29 36 51 70 89 90 94—97 101—104 118 119 129 159
Mirsky, L. 31 53 65 71 75 77 89 91 92
Mixed volume 29 90
Mlak, W. 133 154 162
Moffert, C.F. 61 88
Mohr, E. 46 54
moment 99
Moment sequence 102 112
Moment space 28 39 45 99 102—110
Moment, trigonometric 99
Montroll, E.W. 80 92
Morgenstern, O. 81 83 94 120 129 130
Motzkin, T. 119 129 145 160
Moyal, J.E. 55
Moyls, B.N. 79 92
Murdock, L. 113 128
Murnaghan, F.D. 38 53
Murray, F.J. 94
Narasimhan, R. 154 162
Nemyckii, V.V. 135 158
Nerlove, M. 81 94
Nevanlinna, R. 115 128
New inequalities from old 46 47
Newman, J. 130
Newton, I. 53 163
Neyman — Pearson lemma 121—123
Neyman, J. 101 121 126
Nikaido, H. 119 130
Nirenberg, L. 165 185
Noll, W. 46 54
Nonconvex space 105 115 116
Noneuclidean geometry 39
Nonlinear function, as envelope of linear functions 23
Nonnegative definite matrix 57
Nonnegative definite matrix, principal minors of 58
Nonnegative matrix 93
Norm 16 28
Northcott — Bellman inequality 183 184
Northcott, D.G. 166 182 183 186
Nurenberg, L. 133 148 161 168
Ogura, K. 23 51
Olkin, I. 2 48 49 54 55 64—66 88—90 97
Operator inequality 131
Operator, adjoint 79
Operator, differential 131—134 142—144 164—188
Operator, dissipative 88
Operator, parabolic 150—153
Operator, partial differential 132
Operator, positive 56 93 131 140 147—
Operator, variation-dimishing 86 87 133
Opial, Z. 137 159
Oppenheim's inequality 71
Oppenheim, A. 71 91
Orden, A. 120 129
Order-disorder theory 113 128
Orthant 84 93
Orthogonal matrix 93
Orthogonal projection 123 124
Osserman, R. 157 163
Ostrowki's inequality 32
Ostrowski — Taussky inequality 59
Ostrowski, A. 1 30—32 52 59 62 64 78 86 88—90 95 166 182 184 186 188
Parabolic operator 150—153
Parker, W.W. 86 95
Parodi, M. 146 161
Parseval's equation 178
Parseval, M.A. 175 178
Partial differential equation 180 181
Partial differential inequality 146 163
Partial of hyperbolic type 85
Payne, L.E. 157 164
Pearson, E. 101 121 126
Peixoto, M. 132 145 160
Perron, O. 56 80 93 94 118 129 137 139 159
Petersson, H. 132 144 147 159
Petrov, V.N. 132 143 146 159
Phillips, R.S. 88 97
Picard, E. 100 112 114 116 127
Pick, G. 2 39 43 44 53 115 128
Picone, M. 130
Pitt, H.R. 166 186
Plancherel, M. 175
Pluecker, J. 92
Poincare, H. 75 91 132 144 158 165
Poisson, S.D. 90
Polar function 28 29
Pollak, H. 178 187
Polya, G. 1 31 32 39 44 50—54 60 61 76 91 97 111—113 129 132 143—149 157 158 161—166 177—182 186
Polygonal inequality 183
Polynomial, hyperbolic 36—38 85 90
Positive definite function 100 114 115
Positive definite matrix 3 55—64 87
Positive definite matrix, as sum of squares 58 59
Positive definite matrix, principal minors of 57—59
Positive definite quadratic form 55 112
Positive definite sequence 113 114
Positive function 99
Positive indefinite matrix 57
Positive matrix 56 80
Positive operator 56 93 131 140 147—157
Positive real function 86
Positive transformation 56
Positivity, domain of 56 87 88
Potential equation 153
Price, G.B. 90
Pringsheim, A. 51
Probability theory 55
Prodi, G. 133 154 162
Programming, dynamic 85
Projection technique 98 123 124
Protter, M.H. 162
Pucci, C. 133 154 162 186
Quadratic form 3
Quadratic form, canonical representation 68 69
Quadratic form, Hermitian 57
Quadratic form, indefinite 38 39
Quadratic form, positive definite 57
Quasi linearization 23—33 52 139 155 156
Quasi linearization of convex and concave functions 29 30
Rado, T. 146 160
Raikov, D. 100 114
Rational betting 120
Rational polynomial 111—112
Rayleigh quotient 71 72
Rayleigh, J.W.S. 71
Reade, M. 146 160
Redheffer, R. 133 157 163 164
Reid, W.T. 132 145 160 165 166 180 186
Relativity theory 38 39
Representation for arithmetic-mean — geometric-mean inequality 9
Representation for Cauchy's inequality 3
Representation for integrals 61
Representation for matrices 58—61 63 66 67 70
Representation for matrices hermitian 65
Representation for positive definite functions 100
Representation for quadratic forms 58 59
Representation for quadratic, canonical 68 69
Representation in quasi linearization 23—32
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