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| Авторизация |
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| Corduneanu C., Gheorghiu N., Barbu V. — Almost Periodic Function |
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| Предметный указатель |
 -almost periodic 173
 -approximate mean value 193
-decomposition 187 192
Almost periodic function in a half-plane 137
Almost periodic function in a strip 83 89 134—136
Almost periodic function in probability 70
Almost periodic function of an integer variable 45
Almost periodic function on groups 186
Almost periodic function on topological groups 210
Almost periodic function, analytic 76
Almost periodic function, definition 9 153
Almost periodic function, derivative of 13 27 58 66 69
Almost periodic function, function of 13 61
Almost periodic function, fundamental properties 9
Almost periodic function, harmonic 133
Almost periodic function, in the mean 62 69 142 150 172
Almost periodic function, mean value of 23
Almost periodic function, on the left (right) 186
Almost periodic function, polyharmonic 133 139
Almost periodic function, primitive of 27 98 175 177
Almost periodic function, sequence of 12 25 57 65 134 139 155
Almost periodic motion 124
Almost periodic representation 196
Almost periodic sequence, numerical 45
Almost periodic sequence, properties 46
Analytic almost periodic function 76 83
Analytic extension to half-plane 91
Analytic function in a half-plane 77 93
Analytic function in a strip 79
AP(X) 158
Approximation in the mean 63
Approximation property 10 154 158
Approximation theorem 160 203
Approximation theorem, Weierstrass 216
Asymptotically stable 124
Banach space 153
Basis 41
Behavior at infinity 93
Bessel’s inequality 4 28 202
Biharmonic function 131
Bochner summation 167
Bochner — Fejer polynomials 89 169
Bogoliuboff, N. N. 9
Bohr’s definition 14 153 215
Bounded in a strip 131
Bounded in the mean 63
Bounded representation 196
Bounded solutions 105 112
Compactness criterion 158
Completely continuous operator 204
Conformal mapping 136
Continuous linear functional 167
Convergence of Dirichlet series 92
Convergence of Fourier series 31 44
Convergent in the mean 39
Dense, relatively 154
Derivative 13 27 58 66
Differentiation of Fourier series 27
Diophantine inequalities 163
Dirichlet coefficients 88
Dirichlet coefficients, convergence of 92
Dirichlet coefficients, exponents 88 93
Dirichlet coefficients, negative 91 96
Dirichlet coefficients, series 87
Doetsch’s theorem of three straight lines 80
Dual space 167
Eigenvalues of linear systems 105—106
Equi-almost periodic 38 159
Equi-continuous 38 159
Equivalent representation 196
Exponential polynomials 79
Favard, J. 119 128 136
Fejer kernel 41
Fejer summability 38
Fourier coefficients, cardinality 26 165
Fourier coefficients, cardinality, minimum property 25
Fourier exponents, limit point of 36 38
Fourier exponents, limit point of, linearly independent 44
Fourier series 2 23 160 167 196 202
Fourier series, convergent 31 44
Fourier series, differentiation of 27
Fourier series, integration of 27
Fourier series, summability 38
Fourier series, uniform convergence 30 44
Fourier transform 7
Function analytic in a strip 79
Function of an almost periodic function 13
Function vanishing in a strip 81
Generalized solution 141—142
| Generating system 108
Graph 109 113
groups 186
h-translate 153
Hahn — Banach theorem 168
Half-plane 77
Harmonic function 128 133
Harmonic function, bounded 130
Harmonic in a half-plane 137
Harmonic in a strip 130 135—136
Hyperbolic equation 140
Integration of Fourier series 27
Irreducible family 199—200
Irreducible unitary representation 201 211
Kernel, Fejer 41
kronecker 163
Linear functional 167 195
Linear oscillations 107
Linear representation 196
Linear system 100 119
Linear system, eigenvalues of 105—106
Linear system, solution of 104
Linear transformation, reducible family 199
Linearly independent numbers 40
Matrix, triangular 100
Mean value of almost periodic function 23
Mean value of almost periodic function, 186 192 194
Mean value, -approximate 193
Motion, almost periodic 124
Muckenhoupt, C. F. 62 172
Nicolescu, M. 132
Nonlinear oscillations 112 119
Nonlinear system 120
Normal function 14 45 58 154 156
Normal in probability 73
Normal in the mean 67
Numerical almost periodic sequence 45
Operator, completely continuous 204
Ordinary differential equation 98
Oscillations, linear 107
Oscillations, linear, nonlinear 112 119
Parabolic equation 144
Parameters 55
Parseval’s formula 4 28 207
Partial differential equation 128
Periodic function 1
Poisson’s formula 129
Polyharmonic almost periodic function 139
Polyharmonic function 128 131 133 139
primitive 27 98 175 177
Quasilinear systems 108
Random function 69ff
Random trigonometric polynomial 74
Recurrent system 145
Reducible family 199
Relatively dense 154
Representation, almost periodic 196
Representation, almost periodic, bounded 196
Representation, almost periodic, equivalent 196
Representation, almost periodic, linear 196
Representation, almost periodic, unitary 196
Separated in Z 113
Separated solution 113 116
Sequence in a strip 84
Sequence of almost periodic functions 12 25 39 52 57 65 134 155
Sobolev, S. L. 141
Spectral characterization 52
Stable, asymptotically 124
Stepanov 172
Strip [a,b] 19
Structure theorem 132
Sturm — Liouville system 140 142
Successive approximations 109
Summability of Fourier series 38 167
Topological group 189 210
Topological group, precompact 190
Trajectory 121
Translation number 14 55 68 154
Triangular matrix 100
Trigonometric polynomial 9 62 153
Trigonometric polynomial, sequence of 41
Trivial solution 119
Uniform convergence in probability 72
uniform convergence of Fourier series 30
Uniqueness theorem 2 29 88 167 203
Vector almost periodic function 60
Weakly almost periodic function 175
Weakly continuous 176
Weierstrass approximation theorem 216
Zeros of f(z) 96
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