Dym H., McKean H. — Fourier Series and Integrals (Probability & Mathematical Statistics Monograph) :: Электронная библиотека попечительского совета мехмата МГУ

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Dym H., McKean H. — Fourier Series and Integrals (Probability & Mathematical Statistics Monograph)

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Название: Fourier Series and Integrals (Probability & Mathematical Statistics Monograph)

Авторы: Dym H., McKean H.

Аннотация:

The ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics. Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier's basic series and integrals and on the astonishing variety of applications in which it is the chief tool. It presents a mathematical account of Fourier ideas on the circle and the line, on finite commutative groups, and on a few important noncommutative groups. A wide variety of exercises are placed in nearly every section as an integral part of the text.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1972

Количество страниц: 301

Добавлена в каталог: 17.04.2014

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Предметный указатель

Munroe, M.E.      5
Nagell, T.      223
Negative operator      57 74—75
Negative operator, Laplacian as      245 265 277
Neugebauer, O.E.      1
North pole      229 232—233 252
Observable      117—118
Orbit      233
Orthogonal      22
Orthogonal matrix      228—229
Outer functions (filters)      172—176 193—194
Palermo, C.      221
Palermo, R.      221
Paley — Wiener theorem      158—161
Paley, R.E.A.C.      144 162 169 282
Papoulis, A.      282
Parseval's identity (formula)      27 92 116 269
Partial differential equations      see "Heat equation" "Wave
Partial fraction expansion      154
Permutation      134 204—206
Perpendicular      15 see in "Unit-perpendicular
Perpendicular family      22 218 246—247 257 260—261
Perpendicular splitting of $L^{2}$       98 164 208 210
Perpendicular sum of spherical harmonics      252 272—273 279
Phase delay      175—176
Phase shift      170 172
Phragmen — Lindeloef theorem      155—156 157 159 160
Piecewise smooth curve      145
Placzek, G.      184
Plancherel identity (formula) for $L^{2}$ of an interval      25—27
Plancherel identity (formula) for $L^{2}$ of Euclidean n-space      132—133 138 272
Plancherel identity (formula) for $L^{2}$ of finite commutative groups      219
Plancherel identity (formula) for $L^{2}$ of noncommutative groups      227 256 261 278—280
Plancherel identity (formula) for $L^{2}$ of radial functions      133 268
Plancherel identity (formula) for $L^{2}$ of the line      88—91 94 97 106 119 161
Plancherel identity (formula) for $L^{2}$ of the nonstandard torus      85
Plancherel identity (formula) for $L^{2}$ of the torus      81
Plancherel identity (formula) for $L^{2}$ of the unit circle      3 30 47 48 72 208
Poisson representation formula for disc      36 193—194
Poisson representation formula for half-plane      164
Poisson summation formula      111—112 139—140 141 219—221
Pole      153—154
Pollack, H.O.      122 130
Pontrjagin duality theorem      207
Positively directed curve      145
Power series      151—154
Prime number theorem      196—202
Projection      25 28—29 122—123 175 184 187 271 279
Projective space      230—231 260
Pyatetskii-Sapiro, I.I.      261 281
Quadratic nonresidues      223
Quadratic reciprocity      222—226
Quadratic residues      222—223
quantum mechanics      117—119
Rademacher functions      222
Rademacher, H.      141 222 223
Radial functions      132—134 268
Radiative equilibrium      177—178
Radon transform      137—139
Random flights      142—143
Random walk      82—84 142 185
Rapidly decreasing      34 87 93 100
Rauch, H.E.      79
Rayleigh, Lord      142
Redheffer, R.      144
Reducible-representation      227
Region      144
Representation, of groups      227 255—261
Residue      154
Riemann      2
Riemann integration      5—7 9
Riemann zeta function      197—202
Riemann — Lebesgue lemma      39 40 96 102 105 199
Riesz representation theorem      29 38 see "Exercise
Riesz — Fischer theorem      3 26 27
Riesz, F.      29
Rigid motions of hyperbolic plane      273—274
Rigid motions of line      262
Rigid motions of plane      261 263
Robbins, H.      196
Robin, L.      123 281
Robinson, E.A.      175 176
Rogozinsky, W.      282
Ross, K.A.      282

Rota, G.-C.      74 80 187 214
Rotation group      228—236
Rovnyak, J.      194
Royden, H.L.      5
Rudin, W.      5 144 282
Ruehl, W.      281
Sampling formula      129—132
Sapiro, Z.Ya.      229 256
Schaar — Landsberg identity      225—226
Schreiber, M.      x
Schwarz's inequality      14 16
Schwarz, L.      196
Seeley, R.      253 282
Selberg      4 196
Separable      13 20 28—29 37 210
Shannon, C.E.      130 131
Siegel      140
Signature (of permutation)      134 206
Simple curve      145
Sine integral      92—93 134 263
Sine series      57
Skew-symmetric matrix      231
Slepian, D.      122
Sommerfeld, A.      61 66 68 135
span      23 29 see in "Perpendicular" "Unit-perpendicular
Span of characters of representations      258—261
Span of spherical functions and their translates      242 247 249 268 270
Span of spherical harmonics      252—254
Span of translates of a function      208 211
Span, families which      31 49 79 99—101 165 190 194—196 255
Sparre-Anderson      187
Spectrum      207 210
Speiser, A.      215
Spherical Bessel function      133
Spherical functions      239—249 262 264—268 276—278
Spherical harmonics      249—255 263 268—272 278—279
Spitzer's identity      184—187
Spitzer, F.      184 187
Spur (trace)      59 227 231 256
Stability group      275
Stokes' formula      50
Stromberg, K.A.      5
subspace      28
Swan, D.      61
Symmetric function      134
Symmetric operator      57 60 74 117—118
Sz.-Nagy, B.      29
Szasz — Muentz theorem      194—196
Szegoe theorem      187—194
Szegoe, G.      190
Theta function      52 53 85 112 140
Time-limited function (signal)      121—132 153
Titchmarsh, E.      282
Torus      81 84—85
Trace      see "Spur"
Translation is continuous      39 88
Translation of class functions      260—261
Translation of spherical functions      259—261 268 270
Translation, invariant integration      234—236
Translation, invariant subspaces      207—208 210—211 253
Triangle inequality      15 16 37
Uhlenbeck, G.E.      54
Unit-perpendicular family      22—26 79 165 170 see in
Unitary matrix      256
Van der Waerden, B.L.      228
Vilenkin, N.Y.      256 281
Walsh functions      222
Warnings      12 14 30 90 146 160 207 258
Wave equation      62 70—72 109 135—139
Weierstrass' theorem      49 194 259
Weil      4
Wendell, J.G.      187
Weyl, H.      4 54 117 203 227 228
Wiener — Fourier transform recepe      97—100
Wiener — Hopf factorization      176—184
Wiener — Tauberian theorem      211
Wiener, N.      3 43 98 144 162 169 177 282
Wigner, E.      61
Wilbraham, H.      43
Wirtinger's inequality      47—48 59
Wright, G.M.      222
Yosida, K.      80
Zeeman effect      251 256
Zeta function (Riemann's)      197—202
Zygmund, A.      144 282

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