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Levin B.Ya. — Lectures on entire functions

Levin B.Ya. — Lectures on entire functions

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Название: Lectures on entire functions

Автор: Levin B.Ya.

Аннотация:

The aim of the monograph is to expose the main facts of the theory of entire functions and to give their applications in real and functional analysis.
The general theory starts with fundamental results on the growth of entire functions of finite order, their factorization according to Hadamard's theorem, properties of the indicator, and theorems of the Phragmen-Lindelof type.
Numerous applications include Riesz' bases formed by exponential functions, completeness and minimality of special systems of functions, quasianalyticity of lacunar Fourier series and infinitely differentiable functions, the Titchmarsh convolution theorem, mean-periodic functions, interpolation in spaces of entire functions, the uniqueness problem for Fourier series and infinitely differentiable functions, Bernstein's inequality for the derivative of an entire function, and some properties of Banach algebras.
No special knowledge is required to read this book, except for a standard course of the theory of functions of one complex variable.
The monograph will be useful for graduate students studying the theory of analytic functions, as well as for research mathematicians.

Язык:

Рубрика: Математика/Анализ/Комплексный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 248

Добавлена в каталог: 18.01.2005

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Предметный указатель

-set      86
Agmon S.      161
Ahlfors L.      78 191
Ahlfors theorem      191
Akhiezer N. I.      162 189 227 230 235 236
Approximate identity      139
Avetisyan A. E.      51
Azarin V. S.      78 96 113 119
Babenko K. I.      200 204 206
Babenko — Dzhrbashyan theorem on nontriviality of class       206
Babenko’s theorem      200
Ber G. Z.      159 162
Berenstein C      124
Bernstein interference theorem      162
Bernstein S. N.      150 160 162 227 236
Bernstein V.      55
Bernstein’s inequality      227
Bernstein’s inequality, generalized      232
Beurling A.      40 122 132 133 195 197 213
Beurling’s theorem      197
Bieberbach L.      73
Blaschke product      104
Blaschke W.      104
Boas R. P.      160 162
Boas — Bernstein interpolation theorem      160
Bonsall F. F.      236 238
Borel E.      18 28 30 65
Borel transform      65 69
Borichev A. A.      119
Bourbaki N.      41
Browder A.      236
Brudnyi Yu. A.      41
Caratheodory C.      75
Caratheodory’s inequality      75
Carleman T.      105 107 187 209 213
Carleman — Ostrowski theorem      106
Carleman, formula      187
Carleman, transform      122
Carleman’s theorem      105
Carlson F.      58 71 189
Carlson, analytic continuation theorem      71
Carlson, uniqueness theorem      58
Cartan H.      12 76 78
Cartan’s estimate      77
Cartwright class      97 115
Cartwright M. L.      127 160
Cartwright — Levinson theorem      127
Cartwright’s theorem      160
Chebotarev N. G.      221 222 225
Class, $(\Lambda)$ -quasianalytic      105
Class,       204
Class,       199
Class, (I)-quasianalytic      15
Class, C      115
Class, P      217
Completeness of a system of exponentials      19 84 132
Completeness of a system of functions      22
Completeness, twofold      181
Continuation analytic      70
Davydova E.      161
de Branges L.      130 220
Density, angular      95
Density, lower      17
Density, maximal      132
Density, upper      17
Din Than Hoa      162
Domar Y.      119
Duffin R. J.      230
Duncan T.      238
Dzhavadov M. G.      183
Dzhrbashyan M. M.      51 166 195 204 206
Dzhrbashyan uniqueness theorem      196
Dzhrbashyan’s theorem on triviality of class       199
Element Hermitian      236
Entire function of completely regular growth      94
Entire function of exponential type (EFET)      4
Entire function of finite order      3
Entire function of integer order      32
Entire function of noninteger order      31
Entire function with zeros on a ray      81
Entire function, admitting a lower bound      209
Entire function, sine-type      163
Entire functions with values in Banach algebras      40
Eremenko A. E.      165 Essen M.
Evgrafov M. A.      40
Exponent of convergence      17
Function, $\rho$ -trigonometric      53
Function, $\rho$ -trigonometrically convex      54
Function, admitting positive harmonic majorant      102
Function, counting      10
Function, counting for half-plane      188
Function, harmonic in the upper half-plane      209
Function, harmonic, positive      100
Function, logarithmically subharmonic      50
Function, mean periodic      121
Function, subharmonic      45
Function, supporting      63
Functional analytic      73
Garnett J. B.      141 145 146 179
Gasymov M. G.      183
Gauss theorem      231
Gelfand and Shilov uniqueness problem      204
Gelfand I. M.      41 42 44 119 199 204 237
Gelfand problem on invariant subspaces      119
Gelfond A. O.      22
Genus of a canonical product      26
Genus of an entire function      27
Gohberg I. Z.      121 169 171 184 215
Goldberg A. A.      13 57 118 149 188
Golovin V. D.      170
Golovin’s theorem      170
Gorin E. A.      41 78 238
Govorov N. V.      57
Grabb M. T.      236
Grishin A. Ph.      57 113 149
Gurarii V. P.      183
Hadamard factorization theorem      26
Hadamard J.      18 26 31 48 105
Hardy G. H.      50 60
Hardy space      137
Hardy’s theorem      60
Harmonic majorant principle      46
Havin V. P.      195
Hayman W. K.      13 40 45 49 57 97 109 112 113
Hayman’s theorem      109
Herglotz G.      99
Hermite Ch.      222
Hermite — Biehler theorem      222
Hermite — Biehler theorem, generalized      222
Higgins J. R.      151
Hilbert transform      145
Hilbert transform, discrete analogs      159
Hormander L.      197
Hruscev S. V.      178
Indicator diagram      65
Indicator diagram, conjugate      65
Indicator function      53
Ingham A.      177
Ingham’s theorem      177
Interference phenomenom      162
Jensen formula      10 48
Jensen formula, generalized      125
Jensen J. L. W. V.      9 10 48
Joricke B.      195
Kadets M. I.      172
Kahane J.-P.      124
Katsnelson V. E.      172 236
Katsnelson’s theorem on Riesz base of exponentials      172
Katsnelson’s theorem on spectral radius of Hermitian element      236
Katznelson Y.      203

Keldysh M. V.      181
Kennedy P. B.      45 49
Khabibullin B. N.      85 130
Kheifits A. I.      168
Khurgin Ya. I.      151
Kjellberg B.      40
Koldobskii A. L.      78
Koosis P.      16 130 133 135 141 145 146
Korevaar J.      135
Kostyuchenko A. G.      183
Kotelnikov V.      151
Krasichkov-Ternovskii I. F.      133 212
Krein M. G.      44 115 118 121 169 171 184 215 218 220 222
Krein simple fractions series theorem      116
Krein’s theorem on functions of class C      115
Krein’s theorem on meromorphic functions with interlacing zeros and poles      220
Laguerre E.      28 220
Landkof N. S.      49 78
Laplace transform      67
Le Page C.      41 43
Leau L.      72
Legendre transform      195
Leontev A. F.      84 149
Levin B. Ya.      16 55 78 96 149 161 162 168 220 225 236
Levinson N.      16 127 135 213
Lindelof E.      1 33 37 55 93
Lindelof’s theorem      33 93
Logvinenko V.      161
Lower bound for harmonic function      76
Lower bound for logarithmic potential      77
Lower bound for the modulus of an analytic function      79
Luxemburg W. A. J.      51
Lyubarskii Yu. I.      184
Lyubich Yu. I.      107 122
Malliavin P.      85 132 133 161
Mandelbrojt Sh.      107 203 204 206
Markus A. S.      184
Markushevich A. I.      22
Matsaev V. I.      118 209 212 214
Matsaev’s theorem      209 214
Maximum principle      37
Meiman N. N.      222 225
Mergelyan S. N.      85
Miintz Ch. H.      103
Minkin A. M.      179
Mogulskii E. Z.      212
Montel P.      221 222
Morgan G. W.      59 197
Morgan’s theorem      59
Muckenhoupt B.      179
Muckenhoupt condition      179
Muntz theorem      103
Nazarov F. L.      61 195
Nevanlinna F.      189 190
Nevanlinna F. and R. theorem      189
Nevanlinna R.      10 12 13 78 99 105 187 189 190 192 209
Nevanlinna, characteristic      12
Nevanlinna, class      116
Nevanlinna, first theorem      12
Nevanlinna, formula      187
Nevanlinna, formula for a half-disk      192
Nevanlinna, formula for functions with positive imaginary parts      100
Nevanlinna, representation of functions with positive harmonic majorants      105
Nikolskii N. K.      121 178 212
Operator interference      162
Operator preserving inequality      230
Order of an entire function      3
Ostrovskii I. V.      13 57 118 119 149 188
Ostrowski A. M.      105 204
Ostrowski function      204
P-majorant      227
Palamodov V. P.      204
Paley R. E. A. C.      69 133 146 172
Paley — Wiener, -theorem      146
Paley — Wiener, on minimality      133
Paley — Wiener, theorem      69
Pavlov B. S.      178
Phragmen E.      1 37
Phragmen — Lindelof theorem      37
Phragmen — Lindelof theorem in F. and R. Nevanlinna form      190
Phragmen — Lindelof theorem in integral form      50
Pichorides S. K.      144
Plancherel M.      50 152 161
Plancherel — Polya, equivalence norm theorem      161
Plancherel — Polya, interpolation theorem      152
Poisson formula      9
Poisson — Jensen formula      9
Polya G.      15 40 50 63 132 152 161 220
Polya’s theorem on (I)-quasianalyticity of lacunary Fourier series      15
Polya’s theorem on conjugate diagram      66
Potential logarithmic      48
Privalov I. I.      146
Product absolutely convergent      25
Radius spectral      42
Rafaelyan S. G.      166
Raikov D. A.      41 44
Rashkovskii A. Yu.      213
Redheffer R. M.      135 203
Riesz F.      48 99
Riesz F., measure      48
Riesz F., theorem      48
Riesz M.      142 169
Riesz M., base      169
Riesz M., theorem      142
Riesz — Herglotz formula      99
Ronkin L. I.      45 49 96
Rubel L.      85
Rudin W.      41 44
Russakovskii A. M.      149
Sampling theorem      150
Schaeffer A. C.      230
Schwartz L.      121 122 124
Schwarz formula      9
Seip Kr.      179
Set of finite view      109
Shannon C. S.      151
Shilov G. E.      41 44 58 199 204
Shilov’s theorem      58
Shkalikov A. A.      183 184
Sinclair A. M.      236
Sodin M. L.      165
Space, $A^{\ast}(D)$       73
Space, $B_\sigma$       150
Space,       137
Space, $H^p_{_}$       145
Space, $L^p_{\sigma}$       149
Space, $L_\sigma$       150
Space, A(D)      20
Spectral synthesis      122
System minimal      131
Szego G.      40
Taylor B. A.      124
Theorem on a segment on the boundary of the indicator diagram      83 85
Theorem on addition of indicators      118
Theorem on completeness and minimality of exponentials      134
Theorem on division      80
Theorem on three circles      48
Theorem on two constant      92
Timan A. F.      227
Titchmarsh convolution theorem      119
Titchmarsh E. C.      119
Tkachenko V. A.      107 122
Tsuji M.      40
Type of function      4
Type, exponential      4
Type, maximal      4
Type, mean      4
Type, minimal      4
Type, normal      4
Ulanovskii A. M.      119

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