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Levin B.Ya. — Lectures on entire functions
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Название: Lectures on entire functionsАвтор: 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.
Язык: Рубрика: Математика /Анализ /Комплексный анализ /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1996Количество страниц: 248Добавлена в каталог: 18.01.2005Операции: Положить на полку |
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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, 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, 53 Function, 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, 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, 73 Space, 150 Space, 137 Space, 145 Space, 149 Space, 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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