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| Steele J.M. — Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities |
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| Предметный указатель |
Order relationship, systematic exploitation 73
Order-to-quadratic conversion 78 287
Orthogonality, definition 58
Orthonormal 217
Orthonormal sequence 70
Other inequality of Chebyshev 77
Parameterized parameters 164
Persson, L.E. 288 289
Pillars, three great 87
Pitman, J. 190 276
Plummer, M.D. 278
Poelya — Szegoe converse 83
Poelya's dream 23
Poelya's questions 30
Polarization identity 49 70
Polya, George 30 197 286
Positive definite 228
Power mean continuity relations 127
Power mean curve 124
Power Mean Inequality 123
Power mean inequality, simplest 36
Prekopa — Leindler inequality 287
Principle of maximal effectiveness 27
Principle of similar sides 139
Probability model 17
Product of linear forms 59
Projection formula 56
Projection formula, guessing 58
proportionality 50
Proportionality, gages of 39
Proschan, F. 277
Ptak, V. 247
Ptolemy inequality 69
Pythagorean Theorem 47 51
Qian, Z. vi
Quadratic form 228
Quadratic inequality 76
Qualitative inference principle 3 27
Quasilinear representation, geometric mean 259
Rademacher— Menchoff inequality 217 223
Ratio monotone 189
Reflection 60
Reznick, B. vi
Richberg, R. 272
Riesz proof of Minkowski inequality 141
Riesz, F. 288
Riesz, M. 288
Rogers inequality 152 153
Rogers, L.C. 135 152 290
Rolle's theorem 102 251
Rosset, S. 290
Rousseau, C. 264
Rule of first finder 12
Schur convexity 191
Schur convexity, defined 192
Schur criterion 193
Schur inequality 83
Schur's lemma 15
Schur, Issai 192
Schwarz inequality 10 11
Schwarz inequality, centered 115
Schwarz inequality, pointwise proof 115
Schwarz's argument 11 63
Schwarz's argument in inner product space 15
Schwarz's argument in light cone 63
Schwarz's argument, failure 136
| Schwarz, Hermann Amandus 10
Selberg inequality 225
Self-generalization 21
Self-generalization, Cauchy inequality 16
Self-generalization, Cauchy — Schwarz inequality 66
Self-generalization, Hoelder's inequality 151
Seymour, P.D. 289
Shaman, P. vi
Sharpley, R. 288 289
Shen, A. 231
Shepp, L. vi
Shparlinski, I.E. vi 281
Siegel's method of halves 122
Siegel, Carl Ludwig 122
Sigillito, V.G. 244
Simonovits, M. 277
Skillen, S. vi
Slip-in trick 117
Sphere arrangement 52
Splitting trick 106 123 147 154 227 263 267
Splitting trick first used 12
Splitting trick grand champion 266
Splitting trick, defined 226
Stability in Hoelder inequality 145
Stability of AM-GM inequality 35
Steepest ascent 67
Stefanescu, D. 262
Stress testing 268
Stromberg, K. 243
Sum of squares 42–44 46
Superadditivity, geometric mean 34 100 133
Symmetry and reflection 62
Szego, Gabor 234
Szemeredi regularity lemma 205
Tang, H. vi
Telescoping 29
Thinking outside the box 52
Three Chord Lemma 104
Tilde transformation 193
Tiskin, A. 231
Toeplitz method 165
Treibergs, A. 242
Triangle inequality 54
Unbiased estimator 17
van Dam, E.R. 230
van der Corput inequality 214
van der Corput, J.G. 214
Variance 18 116
Vaughn, H.E. 278
Vince, A. 81
Vinogradov, I.M. 281
Vitale identity 133
Vitale, R. vi
von Neumann, John 51 286
Wagoner, S.S. 238
Walker, A.W. 192
Ward, N. vi
Watkins, W. 277
Weierstrass inequality 190
Weitzenboeck inequality 93 102
Weyl, H. 206 288
Wiles, Andrew 40
Wilf, H. vi 235
Young inequality 136
Zuckerman, H.S. 260
Zukav, G. 286
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