| Preface |
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vii | |
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Notation and some preliminaries from analysis |
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1 | (10) |
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1 | (1) |
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2 | (2) |
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4 | (1) |
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Interpolation of linear operators |
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5 | (1) |
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6 | (1) |
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7 | (1) |
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8 | (3) |
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10 | (1) |
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Distribution of zeros of finite Fourier (Laplace) transforms |
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11 | (30) |
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On zeros of finite Laplace transforms |
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11 | (5) |
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On zeros of Fourier sine- and cosine-transforms |
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16 | (9) |
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Bounds for zeros of the finite Laplace transforms |
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25 | (6) |
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A condition for all the zeros of an entire function of exponential type to lie in a curvilinear half-plane |
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31 | (10) |
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Comments and supplements to
Chapter 2 |
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39 | (2) |
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Estimates of Fourier and Laplace transforms and their applications |
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41 | (24) |
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Asymptotic behaviour of finite Laplace transforms |
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41 | (11) |
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Complex variants of the Abelian theorem for Laplace transforms |
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52 | (3) |
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Decreasing finite Fourier transforms and their application to the approximation |
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55 | (5) |
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Finite Fourier transforms without zeros in a neighbourhood of the real axis |
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60 | (5) |
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Comments and supplements to
Chapter 3 |
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63 | (2) |
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Laplace transforms in the weight spaces Lp and their applications |
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65 | (18) |
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Laplace transforms as operators in the spaces Lp∞ |
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65 | (4) |
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On completeness and non-minimality of a system of exponents in Lp(-π,π) |
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69 | (14) |
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Comments and supplements to
Chapter 4 |
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81 | (2) |
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Stability of classes of finite Fourier transforms and its application |
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83 | (38) |
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The invariance of the class F L2 |
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83 | (12) |
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The invariance of the class F Lq |
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95 | (6) |
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Entire functions of Bernstein's class that are not Fourier-Stieltjes transforms |
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101 | (10) |
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Excesses of systes of exponents |
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111 | (10) |
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Comments and supplements to
Chapter 5 |
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119 | (2) |
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Non-harmonic Fourier series (behaviour on the initial interval) |
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121 | (28) |
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Formulae for partial sums |
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121 | (6) |
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Non-harmonic Fourier series and the condition (Ap) |
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127 | (10) |
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Equiconvergence and uniform convergence of non-harmonic Fourier series |
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137 | (12) |
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Comments and supplements to
Chapter 6 |
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147 | (2) |
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Non-harmonic Fourier series (behaviour on the real line) |
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149 | (30) |
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Extension of convergence of quasi-polynomials |
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149 | (12) |
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Continuation of functions from the initial segment |
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161 | (3) |
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Convergence and summability of non-harmonic Fourier series in the Lp-norm (1 ≤ p ≤ ∞) on every segment |
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164 | (7) |
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Properties of the system (exp (i(n + β sgn n)t) |
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171 | (8) |
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Comments and supplements to
Chapter 7 |
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176 | (3) |
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179 | (32) |
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The case of real exponents and analysis of the problem in the spaces C and Lp, p > 2 |
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179 | (8) |
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On zeros of analytic functions in a disk |
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187 | (7) |
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Analysis of the problem in the weight spaces Lp |
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194 | (17) |
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Comments and supplements of
Chapter 8 |
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210 | (1) |
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Fourier transforms of rapidly decreasing functions |
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211 | (20) |
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211 | (7) |
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Fourier transforms of rapidly decreasing functions on a half-line and on the line |
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218 | (13) |
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Comments and supplements to
Chapter 9 |
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229 | (2) |
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Approximation by translates and exponents on the line |
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231 | (24) |
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Dense families of translates of a function on a line |
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231 | (14) |
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Approximative properties of weighted exponents on the whole line |
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245 | (10) |
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Comments and supplements to
Chapter 10 |
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254 | (1) |
| References |
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255 | (6) |
| Index |
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261 | |
