Index 387
inverse, 364–369
Fundamental Theorem of Algebra,
18–21
applications, 309–318
to linear differential equations with
constant coefficients, 312–313
linear recurrences, 315–318
to partial fraction expansions,
313–315
to the location of zeros of the
derivative of a polynomial,
309–312
Fundamental Theorem of Calculus
First Form, 5
for complex-valued functions, 27
Second Form, 6
Gauss, Carl Friedrich, 31, 32, 52, 338
geometric progression, 2
Gibbs, Josiah Willard, 88, 378
phenomenon, 79
Girard, Albert, 35
Golay, Marcel Jules Edward, 378
complementary pair, 166
Goldberg, Richard Robinson, 247, 278,
378
Gordan, Paul Albert, 89
Graham, Sidney West, 182, 378
Green, George
theorem, 7
Hahn, Liang-Shin, 31, 378
Hardy, Godfrey Harold, 209, 338, 378
tauberian theorem, 123, 125
heat equation, 211–213
steady state, 211
Heisenberg, Werner Karl
uncertainty principle, 267
Herglotz, Gustav, 247
Hermite, Charles, 89, 379
Hilbert, David, 89
inequality, 217
older, Otto Ludwig, 379
inequality, 325–338
Holt, Emily Marie, 267, 278
Horv´ ath, John, 148, 379
Hunt, Richard Allen, 210, 379
Hurwitz, Adolf, 89
induction
mathematical, 3
weak, 3
well ordering, 3
strong, 3
inequalities, 319–338
inequality
arithmetic–geometric, 319–325
Bernstein, 158–162
Bessel’s, 347
for
L2(T),
136
for
L2(T2),
285
Cauchy’s, 3, 340–341
Cauchy–Schwarz, 135
Hilbert’s, 217
older’s, 325–338
isoperimetric, 218
Minkowski’s, 329
Schwarz, 345
triangle, 6, 10, 26, 346
for
L2(T),
136
Wirtinger’s, 218
Young’s, 325
inner product, 37
integration by parts, 6
Jackson, Dunham, 182, 379
kernel, 176
theorem, 177
Jordan, Marie Ennemond Camille, 134
theorem, 88, 201, 210, 272
Kahane, Jean-Pierre, 182, 379
Katznelson, Yitzhak, 247, 379
kernel
analogue of Fej´ er, 257
Dirichlet, 77, 92
modified conjugate, 85, 151
Fej´ er, 92, 131, 134
conjugate, 107
Jackson, 176
Poisson, 132, 213
positive definite, 239–241
summability, 130, 131
Kolmogorov, Andrey Nikolaevich, 210,
379
Kronecker, Leopold, 66
theorem on Diophantine
approximation, 286
Lacroix, Sylvestre Fran¸ cois, 246
Lagrange, Joseph Louis, 52, 182, 246,
247
Lambert, Johann Heinrich, 67
Laplace, Pierre Simon, marquis de, 246
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