388 Index
laplacian, 211, 247
lattice point, 288
Lebesgue, Henri eon, 102, 106, 379
measure theory, 7–8
point, 8, 103
test, 209
Leibniz, Gottfried Wilhelm von
rule, 6
evy, Paul Pierre, 194, 379
Lindemann, Ferdinand von, 89, 379
linearity
of the Discrete Fourier Transform, 38
of Fourier coefficients, 56
of the Fourier transform, 249
Liouville, Joseph, 89, 379
Lipschitz, Rudolf Otto Sigismund, 184,
209
Littlewood, John Edensor, 338, 378
polynomial, 165–175
tauberian theorem, 125
three principles, 7
logarithm, 25
logarithmic derivative, 310
Lp,
weak type, 106
Maclaurin, Colin, 226
Mahler, Kurt, 242, 244
mathematical induction, 3
matrix
adjoint, 343
circulant, 347
diagonal, 343
Hermitian, 343
orthogonal, 342
symmetric, 342
transpose, 339
unitary, 343
mean
arithmetic, 320
weighted, 323
geometric, 320
weighted, 323
harmonic, 322
Mean Value Theorem of differential
calculus, 4
measure
Mahler, 242
Mehta, Harsh, 134, 379
Minkowski, Hermann, 379
convex body theorem, 288–290
inequality, 329, 331, 338
obius, August Ferdinand, 31
modified Dirichlet kernel, 84
Moivre, Abraham de
formula, 12, 24
Monge, Gaspard, comte de eluse, 246
monotone convergence theorem, 7
Montgomery, Hugh Lowell, 209, 379
Mossinghoff, Michael John, 182, 377
Napoleon’s theorem, 15
von Neumann, John, 52
Newman, Donald Joseph, 194, 379
Newton, Isaac, Sir, 35
Newton–Girard formulæ, 35
Niven, Ivan Morton, 89, 379
norm
Lp, 73
L1, 70
convergence in, 98
q, 140
L1(R), 249
of an algebraic polynomial, 241–246
uniform, 95
Nyquist, Harry, 274
operator, 88
Ostrowski, Alexander Markowich, 32
parallelogram law, 13, 167
Parseval, Marc-Antoine des Chˆenes,
148, 379
Parseval’s Identity, 138–148
for the DFT, 43, 52
in several variables, 280
in several variables, 285
partition of an interval, 5
mesh, 5
Pascal, Blaise
triangle, 292
periodic arithmetic function, 36
Plancherel, Michel, 380
theorem, 265–266, 278
Poisson, Sim´ eon Denis
kernel, 132
olya, George, 338, 378
polynomial
algebraic, 17–21
Bernoulli, 83, 220–229
Chebyshev, 299–308
trigonometric, 76, 77, 149–182
Barker, 166
Beurling, 152
degree of, 76
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