√лавна€    Ex Libris     ниги    ∆урналы    —татьи    —ерии     аталог    Wanted    «агрузка    ’удЋит    —правка    ѕоиск по индексам    ѕоиск    ‘орум   
blank
јвторизаци€

       
blank
ѕоиск по указател€м

blank
blank
blank
 расота
blank
Dym H., McKean H.P. Ч Fourier Series and Integrals
Dym H., McKean H.P. Ч Fourier Series and Integrals

„итать книгу
бесплатно

—качать книгу с нашего сайта нельз€

ќбсудите книгу на научном форуме



Ќашли опечатку?
¬ыделите ее мышкой и нажмите Ctrl+Enter


Ќазвание: Fourier Series and Integrals

јвторы: Dym H., McKean H.P.

јннотаци€:

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.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1972

 оличество страниц: 295

ƒобавлена в каталог: 15.09.2006

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
blank
ѕредметный указатель
Addition formula      249Ч251 262 269Ч270 279
Affine transformation      263
Akhiezer, N.I.      14 29 80 194 196
Algebra      see "Convolution algebra"
Almost everywhere (a.e.)      10
Analytic functions      144Ч156
Anderson, W.N., Jr.      221
Annihilator      28
Antisymmetric function      134
Approximate identity      105
Arithmetic sequence, distribution of      54Ч56
Arthurs, E.      131
Associated Bessel function      268Ч269
Associated conical function      279
Associated Legendre polynomial      253Ч254
Auslander, L.      273
Axis      229Ч232
Bachman, P.      223
Band-limited function      121Ч132
Basis in a Hilbert space      24 26 80 170 255 270 see "Span" "Unit-perpendicular
Basis of eigenfunctions (of Sturm Ч Liouville operator)      73
Basis of Haar functions      27Ч28
Basis of Hermite functions      98
Basis of Laguerre functions      153 165
Basis of Legendre polynomials      36 246Ч247
Basis of prolate spheroidal wave functions      123
Basis of sampling functions      131
Basis of trigonometric functions      30 57 60 81
Basis of Walsh functions      272
Basis theorem, for finite commutative groups      215Ч217
Basis, of skew matrix      231
Bateman, H.      106
Bellman, R.      54 225
Berberian, S.K.      29
bernoulli      2
Bessel equation      133
Bessel functions      132Ч133 143 266Ч267
Bessel inequality      25 27
Bessel transform      132Ч133 267Ч268
Beurling, A.      169
Birkhoff, G.      74 80 203
Bochner, S.      282
Boemer, H.      228 256
Borel measurable set      7
Borel Ч Cantelli lemma      11 19
Cantor set      8
Caratheodory, C.      273
Carleman, T.      169 282
Carleson, L.      34
Carslaw, H.S.      43 44 282
Case, K.M.      184
Cauchy formula      148Ч151 167
Cauchy theorem      145Ч148
Cauchy Ч Riemann equations      148
Central limit theorem      114Ч116 142
Central subgroup      274
Chandrasekhar, S.      142
Chandrasekharan, K.      141 222 282
Character of group      205Ч206 210 218Ч220 222 223 226Ч227 229 232 241 249
Character of representation      258Ч260
ChebyshevТs inequality      11 19
Class function      258
Closed curve      145
Closed subspace      28
Colatitude      233 239
compact function      x 21 37
complete      13 16 37
Conical functions      277
Conjugacy class      258
Convergence in $L^1$      37 38
Convergence in $L^2$      16 18
Convergence, pointwise a.e.      16Ч18
Convolution algebras      41Ч43 87Ч88 103 212Ч213 237Ч239 262 264 277
Coppel, W.A.      2 282
Copson, E.T.      144
Corner      145
Coset      204Ч205
Coset, double      233 262 263 275
Coset, group of      214Ч215 220
Coset, space of      232Ч233 262 263 275
Cosine integral      92Ч93 132 134 262Ч263
Cosine series      60
Courant, R.      ix 49 74 131 196
Crimmins, T.      221
de Branges, L.      194
de Hoffman, F.      184
de la Vallee-Poussin, C.      5
De Moivre      115
Dense      13 21 30 34
Descent, method of      136Ч137
Dimension, of Hilbert space      22 26
DiniТs test      40 105
Direct product, of groups      215
Directed curve      145
Dirichlet      2 105
Dirichlet kernel      31Ч35 40 41 45 260
Divergence theorem      147Ч148
Doetsch, G.      213
Domain      144
Dominated Convergence Theorem      10
Double coset      233 262 263 275
Dual group      206 207 210 218Ч222
Duren, P.      169 194
DТAlembert      1
dТAlembert, formula of      2 71 109 139
Edwards, R.E.      42 43 282
Eigenfunctions (eigenvalues) of Fourier transform      97Ч98
Eigenfunctions (eigenvalues) of integral operators      123Ч126 130Ч131
Eigenfunctions (eigenvalues) of Laplacian      242Ч245 247 251Ч252 265Ч266 268Ч269 270 277 279
Eigenfunctions (eigenvalues) of ordinary differential operators      56Ч60 72Ч80 99 208 211
Eigenvalues      see Eigenfunctions"
Energy of string      72
Entire function      154
Erdoes      196
Ergodic      54
Euclidean motion group      261Ч273
Euler      2
Euler Ч Maclaurin summation formula      112Ч114
Exponential type      155 158
Factor group      214Ч215 220
FatouТs Lemma      10 19
Fejer kernel      35 38 41
Fejer theorem      34Ч36 49 55
Fejer, L.      34 103 106
Feller, W.      53 84 115 187 196
Feynman, R.      x
Filter      170Ч176
Finicky proof      41
Flanders, M.      61
Ford, G.W.      54
Fourier Bessel transform      132Ч133 267Ч268
Fourier coefficient      23 26 39
Fourier cosine integral      92Ч93 132 134 262Ч263
Fourier cosine series      60
Fourier integral      86Ч105 132Ч134 160Ч161 209Ч212
Fourier integral as a rotation      97Ч98
Fourier integral, application of      106Ч116 134Ч143
Fourier integral, growth of      116Ч121 156Ч160
Fourier inversion formula      88 90 94 103 112 132Ч133
Fourier series      30Ч46 81Ч85 206Ч209
Fourier series on finite commutative groups      217Ч219
Fourier series on rotation group      256 261
Fourier series, application of      46Ч72 82Ч84
Fourier sine integral      92Ч93 134 263
Fourier sine series      57
Fourier Ч Legendre series      245Ч249
Fourier Ч Mehler transform      278
Fourier, J.      2 282
Fredholm alternative      60
Frobenius      4 227
FubiniТs Theorem      12 41 102
Fundamental solution, of heat equation      64
Fundamental theorem of algebra      154
Gain      170 172
Gauss      215 222 223
Gauss kernel      104 108 111Ч112
Gauss lattice point formula      140
Gaussian sum      223Ч226
Gelfand, I.M.      229 256 261 281
Gibbs phenomenon      43Ч46
Gibbs, J.N.      43
Ginibre, J.      222
Glazman, I.M.      14 29
Goldberg, R.R.      282
Graev, M.I.      261 281
GrafТs addition formula      269Ч270
Gram Ч Schmidt recipe      25 26 153 247
Green function      58 59 60 64 67 72 80
Group interpretation of classical Fourier analysis      206Ч212
Group, central subgroup of      274
Group, direct product of      215
Group, dual      206 207 210 218Ч222
Group, factor      214Ч215 220
Group, finite commutative      214Ч217
Group, introduction to      203Ч206
Group, orthogonal      228Ч229
Group, permutation      134 204Ч206
Group, representations      227 255Ч261
Group, representations of rigid motions of Euclidean line      262
Group, representations of rigid motions of Euclidean plane      261 263
Group, representations of rigid motions of hyperbolic plane      273Ч274
Group, rotation      228Ч236
Group, special orthogonal      229Ч236
Group, stability      275
Haar functions      27Ч28
Hammermesh, M.      256
Hardy function applications      194Ч196
Hardy function spaces      161Ч176 187Ч194
Hardy, G.H.      3 22 282
Hardy, theorem of      156Ч158
Heat equation      60Ч70 82 107Ч109
Heaviside      213
HeisenbergТs inequality      100 116Ч121 122 156
Heitler, W.      119 251
Helgason, S.      281
Helson, H.      169 194
Hermite function      98Ч101 157 211
Hewitt, E.      5 282
Hilbert space      13Ч15 22 26 29 37
Hilbert transform      93
Hilbert, D.      49 74 131
Hobson, E.W.      2 282
Hoffman, K.      169 194
Homogeneous function      254
Homogeneous polynomial      253 255
Homomorphism, convolution algebra      185 208Ч209 211Ч213 214 239Ч241 249 262 264 273
Homomorphism, group-to-group      204Ч205
Hopf Ч Wiener factorization      176Ч184
Hopf, E.      177 184
Horwitz, H.      221
Hurwitz      49
Hyperbolic distance      274
Hyperbolic plane      273Ч281
Ideal      41
Ikehara, S.      196
Images, Lord KelvinТs method of      66 67 68 108
Improper integral      95Ч96 97 150 151
Indicator functionЧx      9
Infinitely often (i.o.)      11 19
Ingham, A.E.      196
Inner functions (filters)      172 193Ч194
Inner product      13 14 16 22 27 29 218Ч219
Integral function      154
Integration on (other continuous) groups      234Ч236 260 262 264 276
Integration, advantage of Lebesgue theory of      16
Integration, introduction to Lebesgue theory of      5Ч12
Invariant subspace      207Ч208 210Ч211 253
Inverse Fourier transform (formula)      88 90 94 103 112 132Ч133
Irreducible-representation      227
Isomorphic groups      205 207 210 219 220
Isomorphic Hilbert spaces      22 26
Isomorphism between groups      204 207 210 218
Isomorphism between Hilbert spaces      30 272Ч273
Isoperimetric problem      49Ч51
Ito, K.      221
JacobiТs identity      52Ч54 65Ч66 67 85 112
JensenТs Inequality      168 192Ч193
John, F.      ix 137
Kac, M.      106 211
Katznelson, Y.      282
Kelvin, Lord (method of images)      66 67 68 108
Kingman, J.F.C.      187
Kolmogorov, A.N.      34
Lagrange      2
Laguerre functions      153 165
Landau, H.J.      122 130
Landsberg Ч Schaar identity      225Ч226
Laplace      115
Laplace operator      134 242Ч247 251Ч253 255 265Ч266 268Ч271 276Ч279
Laplace transform      213
Lardy, L.J.      213
Latitude      233
Lattice, dual      84
Lattice, GaussТ formula      40
Lattice, MinkowksiТs theorem      140Ч141
Lattice, nonstandard      84
Lattice, random walk on      82Ч84
Lattice, standard      81
Lebesgue      2
Lebesgue integration      5Ч12 16
Lebesgue measurable      7
Leblanc, N.      273
Lee, Y.W.      172
Legendre operator      74
Legendre polynomials      26 242 245Ч249
Legendre symbol      223
Levinson, N.      144 196
LiouvilleТs theorem      154 158
Littlewood      3
Local convergence, of Fourier series      39Ч40
Local-global duality      31 93 106 116
Loomis, L.      282
Ludwig, D.      137
MacLane, S.      203
Maximal invariant subspace      208
Maximum principle for analytic functions      155
Maximum principle for solutions of heat equation      64Ч65
Maxwell equation      256
Maxwell poles      254Ч255
Maxwell, J.C.      254
McKean, H.P.      222
Measurable function      9Ч10 12
Measurable set      7Ч8 12
Measure      7 8 11 12
Mehler transform      278
Mellin transform      103
MercerТs theorem      131
Michaelson, A.      44
MilneТs equation (problem)      176Ч178 181Ч184
Minimal invariant subspaces      208 253
Minimal type      158
MinkowskiТs theorem in the geometry of numbers      140Ч143
MinkowskiТs triangle inequality      16
Minlos, R.      229 256
Moebius function      214 226
Moebius inversion formula      214
Momentum      118
Monotone Convergence Theorem      10 83
MoreraТs theorem      150 152
Mueller, C.      253 256
1 2
blank
–еклама
blank
blank
HR
@Mail.ru
       © Ёлектронна€ библиотека попечительского совета мехмата ћ√”, 2004-2017
Ёлектронна€ библиотека мехмата ћ√” | Valid HTML 4.01! | Valid CSS! ќ проекте