Young R.M. — An Introduction to Nonharmonic Fourier Series :: Электронная библиотека попечительского совета мехмата МГУ

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Young R.M. — An Introduction to Nonharmonic Fourier Series

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Название: An Introduction to Nonharmonic Fourier Series

Автор: Young R.M.

Аннотация:

An Introduction to Non-Harmonic Fourier Series is a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1980

Количество страниц: 246

Добавлена в каталог: 05.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\omega$ -independent      40 46
Absolute basis      3
Absolutely convergent series      2 204
Ahlfors, L.V.      60 225
Akhiezer, N.L.      3 84 213 219 225
Alexander, W.O , Jr.      217 225
Almost periodic exponential sum      84
Almost periodic function      14 206
Amerio, L.      220 225
Anderson, J.M.      213 225
Approximation property      26 205 207
Aronszajn, N.      206 225
Arsove, M.G.      208 225
Arutjunjan, F.G.      204 225
Avdonin, C.A.      221 223 225
Babenko, K.I.      36 208 225
Bade, W.G.      222 225
Banach space      1
Banach — Steinhaus theorem      30
Banach, S.      2 203 207 225
Bari basis      46 51
Bari's theorem      45 210
Bari, N.K.      146 208—210 220 225
Basis      1 203
Basis for      106
Basis problem      2
Basis, absolute      3
Basis, Bari      46 51
Basis, Bessel      36 153
Basis, bounded      31
Basis, conditional      204 208
Basis, equivalent bases      30 208
Basis, for ${A}^{2}$       11
Basis, for ${H}^{2}$       10
Basis, for ${l}^{p}$       2
Basis, for ${L}^{p}[-\pi,\pi]$       203
Basis, for ${L}^{p}[0,1]$       203
Basis, for C[a,b]      3 204
Basis, for P      106
Basis, for the dual space      27—29 207
Basis, Hamel      1
Basis, Hilbert      37 153 167
Basis, normal      26 207
Basis, of eigenfunctions      47
Basis, orthonormal      see “Orthonormal basis”
Basis, perturbation of      see “Stability”
Basis, Riesz      see “Riesz basis”
Basis, Schauder      1 207
Basis, stability of      see “Stability”
Basis, unconditional      3 13 204
Basis, uniqueness of      208
Bellman, R.      221 225
Berberian, S.K.      206 225
Bergman kernel      18 207
Bergman, S.      206 207 225
Bernstein polynomials      3 5 205
Bernstein's inequality      84 86 104 141 212
Bernstein, S.N.      3 84 205 212 213 226
Besicovitch, A.S.      14 206 226
Bessaga, C      203 208 226
Bessel basis      36 153
Bessel functions      68
Bessel sequence      146 153—161 180 220
Bessel sequence, of complex exponentials      162
Bessel sequence, of powers      157
Bessel's inequality      7
Beurling, A.      142 218 226
Billard, P.      204 226
Binmore, K.G.      220 222 226
Biorthogonal sequences      28 29 31 32 36 37 41 51 148 224
Birkhoff — Rota theorem      46 210
Birkhoff, G.      206 210 226
Boas — Pollard theorem      22 207
Boas, R.P., Jr.      101 204 207 209 210 212—215 219 220 226
Bochner, S.      220 226
Bockarev, S.V.      204 226
Bohr, H.      14 206 226
Borel — Caratheodory inequality      75
Borel's theorem      69 211
Borel, E.      54 210 211 226
Boundary function      174
Boundary-value problem      46
Bounded basis      31
Bounded from below      36 157 186
Bounded variation, function of      111
Bounds, for a Bessel sequence      154
Bounds, for a frame      185
Bounds, for a Riesz — Fischer sequence      154
Bourgin, D.G.      209 226
Bratiscev, A.V.      226
Brauer, R      210 226
Byrnes, J.S.      227
Canonical factorization      65
Canonical product      56 69—74
Canonical product, lower bound for      73 211
Canonical product, of genus zero      70 71
Cardinal series      107 109 151 215
Carleman's formula      87—93 115 117 213
Carleman's theorem      114
Carleman, T.      114 213 227
Carleson, L.      9 160 197 201 220 227
Cartwright, M.L.      210 212 227
Ciesielski, Z.      204 208 227
Clarkson, J.A.      213 227
Closed graph theorem      35 169
Closed linear span      27
Closed sequence      see “Complete sequence”
Coefficient functional      22—28 40 207
Compact operator      40 41 45
Complete interpolating sequence      171 175
Complete orthonormal sequence      see “Orthonormal basis”
Complete sequence      6 13 19—22 207
Complete sequence, of complex exponentials      111—143 215—219
Complete sequence, of powers      21
Completeness radius      137—143 166
Conditional basis      204 208
Cook, T.A.      207 227
Corona theorem      160
Cossar, J.      221 227
Curtis, P.C, Jr.      222 225
Dalzell's theorem      15 206
Dalzell, D.P.      206 227
Davie, A.M.      205 227
Davis, P.J.      207 227
Davis, W.J.      209 227
de Branges, L.      214 215 227
Deficiency      113 116 122 143 215
density      138 139 143
Density zero      139
Density, of zeros      90 213
Density, Polya maximum density      138
Density, upper      138
Derivative, of an entire function, inequalities for      84 86 99 104
Derivative, of an entire function, order and exponential type of      67 74
Derivative, of an entire function, zeros of      79
Deutsch, F.      205 227
Diestel, J.      207 227
Dimension, linear      2
Dimension, orthogonal      13
Dirichlet kernel      199
Disk algebra      26 204
Domsta, J.      204 227
Dragilev, M.M.      222 227
Dual space      20 27—29
Dual space, basis for      27—29 207
Duffin — Eachus theorem      44 50 210
Duffin — Schaeffer theorem      190 222
Duffin, R.J.      44 210 212—214 222—224 227
Dunford, N.      206 219 220 227
Duren, P.L.      160 174 204 206 220 227 228

Dvoretzky — Rogers theorem      204
Dvoretzky, A.      204 225
Eachus, J.J.      44 210 227
Earl, J.P.      220 228
Eigenfunction expansion      46 47
Eisner, J.      218 228
Enflo, P.      2 205 228
Entire function, factorization theorems      54—58 74—79
Entire function, interpolation by      58 106 107 151
Entire function, of exponential type      see “Exponential type function
Entire function, of finite order      62—68
Entire function, uniqueness of      see “Uniqueness of
Entire function, zeros of      see “Zeros of
Equiconvergent      197 223 224
Equisummable      201
Equivalent bases      30 208
Equivalent inner products      32
Equivalent sequences      167—170
Erdoes, P.      213 227
Exact frame      186 188 196
Exact sequence      112 126 149 215
Excess      113 137 143 215—218
Exponent of convergence      66
Exponent of convergence, connection with order      66
Exponent of convergence, in terms of n(r)      67
Exponential type      71
Exponential type, function of      53 61
Exponential type, function of, ${L}^{2}$ on the real axis      100—109
Exponential type, function of, ${L}^{p}$ on the real axis      93—100 104 214
Exponential type, function of, almost periodic      84
Exponential type, function of, bounded on a line      80—90 212—214
Exponential type, function of, bounded on a sequence      212
Exponential type, function of, density of zeros      90 213
Exponential type, function of, inequalities for      82 84 94 99 104 107 108 212 213
Exponential type, function of, interpolation by      106—108 151 see
Exponential type, function of, representation by Fourier integrals      101 103
Exponential type, function of, uniqueness of      90—92 105 107 108 111 216
Exponential type, in terms of Taylor coefficients      74
Exponential type, of a derivative      74
Factorization theorems, Hadamard's      74 211
Factorization theorems, Weierstrass's      54 55 211
Fejer — Riesz inequality      161 220
Fejer, L.      220 228
Feller, W.      5 213 228
Finite interpolation      147
Finite moment problem      147
Finite order      63
Finite rank operator      26 205
Fourier coefficients      6 9
Fourier inversion formula      101 150
Fourier series expansion      6 9 197
Fourier series expansion, mean convergence      9
Fourier series expansion, pointwise convergence      9
Fourier transform      9 101 127 142
Fourier transform, inverse      150
Fourier — Stieltjes integral      83 172
Fourier — Stieltjes transform      53
Frame      184—196 222 223
Frame, bounds for      185
Frame, stability of      191—196
Franklin system      204
Fredholm alternative      40 45
free      see “Minimal”
Functional Hilbert space      16—19
Functional Hilbert space, interpolation in      158
Fundamental sequence      see “Complete sequence”
Gamma function      76
Gap theorem, for an entire function      105
Gelbaum, B.R.      208 228
Gelfand, I.M.      208 228
Genus zero      71
Genus, of a canonical product      56
Giroux, A.      213 228
Gohberg, I.C      46 228
Golovin, V.D.      221 228
Gosselin, R.P.      209 228
Gram determinant      147
Gram determinant, generalized      152
Gram matrix      32 157
Gram — Schmidt orthogonalization procedure      15 204
Graves, L.M.      228
Grinblium, M.M.      221 228
Grothendieck, A.      26 205 207 228
Gurarii — Gurarii theorem      209
Gurarii — Meletidi theorem      209
Gurarii, N.I.      209 228
Gurarii, V.L      209 228
Gurevich, L.A.      221 228
Haar system      203
Hadamard's factorization theorem      74 211
Hadamard's inequality      66 69
Hadamard, J.      54 66 74 211 228
Hahn — Banach theorem      20
Hahn, H.      220 228
Halmos, P.R.      40 45 48 206 210 228
Hamburger moment problem      219
Hamburger, H.      219 229
Hamel basis      1
Hammers!ey, J.M.      210 229
Hardy, G H.      10 220 229
Hausdorff maximal principle      13
Hausdorff, F.      219 229
HausdorfT moment problem      219
Hermitian matrix      159
Hilbert basis      37 153 167
Hilbert matrix      158
Hilbert matrix, norm of      161
Hilbert space      6 206
Hilbert — Schmidt operator      45 51
Hilbert's inequality      161 220
Hille, E.      206 229
Hoffman, K.      204 206 216 220 229
Holland, A.S.B.      210 212 229
Holub, J.R.      209 210 232
Hruscev, S.V.      223 229
Hurwitz's theorem      173
Independent      see “Minimal”
Infinite deficiency      143 165
Infinite product      54 211
Ingham, A.E.      220 221 229
Integrability on a line      93—100
Interpolating sequence      171 175 180 183 191
Interpolation      145
Interpolation in      170—184
Interpolation, duality with basis theory      169—171 222
Interpolation, finite      147
Interpolation, in ${B}_{\tau}$       161
Interpolation, in ${E}_{\pi}^{p}$       178
Interpolation, in ${H}^{2}$       158
Interpolation, in a functional Hilbert space      158
Interpolation, inP      170—184 221
Interpolation, solution of minimum norm      147 152
Interpolation, trigonometric      see “Trigonometric moment problem”
James, R.C      206 207 229
Jensen's formula      59—62 119 124 211
Jensen, J L.W.V.      211 229
Johnson, W.B.      207 229
Kac, M.      221 229
Kadec's $\frac{1}{4}$ -theorem      42 122 131 196 210
Kadec, M.I.      210 223 229
Kahane, J.P.      139 218 229
Karlin's theorem, on biorthogonal bases      29 207
Karlin's theorem, on normal bases      26 207
Karlin, S.      203 204 207 229
Karnick, H.      210 233
Katsnelson, V.E.      221 223 229
Kernel function      see “Reproducing kernel”
Knopp, K      211 229
Koosis, P.      139 218 229
KOREVAAR, J.      213 229 231

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