排序方式: 共有27条查询结果,搜索用时 31 毫秒
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Saulius Norvidas 《Lithuanian Mathematical Journal》2014,54(2):192-202
We propose necessary and sufficient conditions for a complex-valued function f on \( {{\mathbb{R}}^n} \) to be a characteristic function of a probability measure. Certain analytic extensions of f to tubular domains in \( {{\mathbb{C}}^n} \) are studied. In order to extend the class of functions under study, we also consider the case where f is a generalized function (distribution). The main result is given in terms of completely monotonic functions on convex cones in \( {{\mathbb{R}}^n} \) . 相似文献
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S. Norvidas 《Acta Mathematica Hungarica》2010,128(1-2):26-35
Let σ > 0. For 1 ≦ p ≦ ∞, the Bernstein space B σ p is a Banach space of all f ∈ L p (?) such that f is bandlimited to σ; that is, the distributional Fourier transform of f is supported in [?σ,σ]. We study the approximation of f ∈ B σ p by finite trigonometric sums $$ P_\tau (x) = \chi _\tau (x) \cdot \sum\limits_{|k| \leqq \sigma \tau /\pi } {c_{k,\tau } e^{i\frac{\pi } {\tau }kx} } $$ in L p norm on ? as τ → ∞, where χ τ denotes the indicator function of [?τ, τ]. 相似文献
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Lithuanian Mathematical Journal - Let f be the characteristic function of a probability measure μf on ?n, and let σ > 0. We study the following extrapolation problem: under... 相似文献
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S. Norvidas 《Lithuanian Mathematical Journal》2006,46(4):446-458
Let, for σ > 0,
be the set of complex functions f ∈ L
1 (ℝ) with the Fourier transforms
vanishing outside the interval [−σ; σ]. In this paper, we study the problem of the best approximation of the Dirac function δ (which has the Fourier transform with widest support supp
) by functions
. More precisely, we consider the quantity inf
and its extremal functions
.
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Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 548–564, October–December, 2006. 相似文献
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Saulius Norvidas 《Lithuanian Mathematical Journal》2017,57(2):236-243
Here we deal with the following question: Is it true that, for any closed interval on the real line ? that does not contain the origin, there exists a characteristic function f such that f(x) coincides with the normal characteristic function \( {\mathrm{e}}^{-{x}^2/2} \) on this interval but f(x) ? \( {\mathrm{e}}^{-{x}^2/2} \) on ?? The answer to this question is positive. We study a more general case of an arbitrary characteristic function g of a continuous probability density, instead of \( {\mathrm{e}}^{-{x}^2/2} \). 相似文献
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Saulius Norvidas 《Lithuanian Mathematical Journal》2011,51(4):522-532
Let K be a compact set in \( {{\mathbb R}^n} \). For \( 1 \leqslant p \leqslant \infty \), the Bernstein space \( B_K^p \) is the Banach space of all functions \( f \in {L^p}\left( {{{\mathbb R}^n}} \right) \)such that their Fourier transform in a distributional sense is supported on K. If \( f \in B_K^p \), then f is continuous on \( {{\mathbb R}^n} \) and has an extension onto the complex space \( {{\mathbb C}^n} \) to an entire function of exponential type K. We study the approximation of functions in \( B_K^p \) by finite τ -periodic exponential sums of the formin the \( {L^p}\left( {\tau {{\left[ { - 1/2,1/2} \right]}^n}} \right) \)-norm as τ → ∞ when K is a polytope in \( {{\mathbb R}^n} \).
相似文献
$ \sum\limits_m {{c_m}{e^{2\pi {\text{i}}\left( {x,m} \right)/\tau }}} $