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Corduneanu C., Gheorghiu N., Barbu V. — Almost Periodic Function
Corduneanu C., Gheorghiu N., Barbu V. — Almost Periodic Function



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Название: Almost Periodic Function

Авторы: Corduneanu C., Gheorghiu N., Barbu V.

Аннотация:

From the Preface: ``The purpose of our book is to provide an overall view of all the basic features of almost periodic functions, in the various meanings this term has acquired in modern research as well as the many applications of such functions. This feature of the book should, of course, make it useful to those readers who are interested in the connections that exist between theory (pure!) of almost periodic functions and such areas of application as the theory of ordinary differential equations and partial differential equations. Several other areas of application are also indicated, together with an abundance of references. The Bibliographical Notes at the end of almost every chapter have been added to in this Second Edition. Completely new is [Chapter II.3], which is devoted to a relatively new class of almost periodic functions: random functions almost periodic in probability. It is certain that these functions will find many applications in the theory of stochastic functional equations.''


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1989

Количество страниц: 257

Добавлена в каталог: 06.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$S^{P}$-almost periodic      173
$\varepsilon$-approximate mean value      193
$\varepsilon$-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, $\varepsilon$-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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