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Beckenbach E.F., Bellman R. — Inequalities
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Название: InequalitiesАвторы: Beckenbach E.F., Bellman R. Аннотация: Since the classic work on inequalities by Hardy, Littlewood, and Polya in 1934, an enormous amount of effort has been devoted to the sharpening and extension of the classical inequalities, to the discovery of new types of inequalities, and to the application of inqualities in many parts of analysis. As examples, let us cite the fields of ordinary and partial differenlial equations, which aie dominated by inequalities and variational principles involving functions and their derivatives; the many applications of linear inequalities to game theory and mathematical economics, which have triggered a renewed interest in convexity and moment-space theory; and the growing uses of digital computers, which have given impetus to a systematic study of error estimates involving much sophisticated matrix theory and operator theory.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1 editionГод издания: 1961Количество страниц: 198Добавлена в каталог: 14.04.2010Операции: Положить на полку |
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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 equation, Kellogg kernel in 96 Integral inequality 21—23 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 Jobn, 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 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 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 Lueroth, J. 51 Lyapunov, A. 92 166 188 Mabler, K. 1 29 51 97 Mac Duffee, C.C. 61 79 88 92 Maclaurin, C. 11 50 Madansky, A. 45 54 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, 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, modular function 90 Matrix, nonnegative 93 Matrix, nonnegative definite 57 Matrix, nonnegative definite, principal minors of 58 Matrix, orthogonal 93 Matrix, positive 56 80 Matrix, positive definite 3 55—64 87 Matrix, positive definite as sum of squares 58 59 Matrix, positive definite, principal minors of 57—59 Matrix, positive indefinite 57 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—157 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 equation of hyperbolic type 85 Partial differential inequality 146 163 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 Plotter, M.H. 162 Pluecker, J. 92 Poincare, H. 75 91 132 144 158 165 Poisson, S.D. 90 Polar function 28 29 Pollak, H. 178 187 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 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 theorem 55 Representation theorem for arithmetic-mean - geometric-mean inequality 9 Representation theorem for Cauchy's inequality 3 Representation theorem for integrals 61 Representation theorem for matrices 58—61 63 66 67 70 Representation theorem for matrices hermitian 65 Representation theorem for positive definite functions 100 Representation theorem for quadratic forms 58 59 Representation theorem for quadratic forms, canonical 68 69 Representation theorem in quasi linearization 23—32
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