Index 389
in several variables, 282
Littlewood, 165–175
PM, 182
Shapiro, 167
ultra-flat, 182
Vaaler, 157
power series, 21–23
power sum, 35
progression
arithmetic, 1
geometric, 2
Pythagorean triangle, 13
Rayleigh, John William Strutt, Lord,
278, 380
rectangle theorem, 27
Rees, Elmer Gethin, 290
rhombus, 14
Riemann, Georg Friedrich Bernhard,
88, 102, 106, 134
Principle of localization, 195
Riemann–Lebesgue Lemma, 59, 102,
106
Riesz, Frigyes, 144, 148, 163, 182, 380
Riesz, Marcel, 134, 380
Riesz–Fischer theorem, 144
Rogosinski, Werner Wolfgang, 209, 378
Rolle, Michel
theorem, 4
Rudin, Walter, 182, 380
Runge, Carl David Tolm´ e, 52
sawtooth function, 58, 62, 78, 79, 151
Schaeffer, Albert Charles, 182, 380
Scheeffer, Ludwig, 194, 380
Schwarz, Karl Hermann Amadeus
inequality, 135, 345
set
convex, 288
symmetric about the origin, 288
Shapiro, Harold Seymour, 182, 380
polynomials, 167
Siegel, Carl Ludwig, 89, 290, 380
singular, 8
Sobolev, Sergei Lvovich, 253, 266
square wave function, 59, 62, 64
Steele, John Michael, 338, 380
sum set, 12
summability
Abel, 123
Ces` aro, 91–110, 121
summability kernel, 130–134
summation formula
Euler–Maclaurin, 226, 278
Poisson, 270–278
in several variables, 288–290
supremum, 72
Tauber, Alfred, 123
tauberian theorem, 123
Hardy’s, 123, 125
Littlewood’s, 125
Titchmarsh, Edward Charles, 278, 380
triangle inequality
for complex numbers, 10
for integrals, 6, 26
for real numbers, 10
trigonometry, 351–374
hyperbolic, 369–374
in calculus, 357–369
in geometry, 351–357
Tubbs, Robert Earl, 89, 377
Tukey, John Wilder, 52, 378
Turyn, Richard Joseph, 182, 380
uniform distribution, 229–238
unimodular, 10
Vaaler, Jeffrey David, 182, 378
polynomial, 157
Vall´ ee Poussin, Charles-Jean
Etienne´
Gustave Nicolas de la
kernel, 133
power kernel, 133
Vaughan, Robert Charles, 209, 379
vector spaces, 339–348
abstract, 344–348
familiar, 339–344
Vinogradov, Ivan Matveyevich, 34
Wagon, Stanley, 32, 380
Wallis, John
formula, 229
wave equation, 213–215
Weierstrass, Karl Theodor Wilhelm, 89,
97, 134
well ordering, 3
Weyl, Hermann Klaus Hugo, 380
criterion, 232, 247
theorem, 234
Whittaker, Edmund Taylor, 278, 380
Wiener, Norbert, 194, 380
theorem on 1/f, 191–193
theorem on translates, 277–278
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