共查询到20条相似文献,搜索用时 15 毫秒
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《复变函数与椭圆型方程》2012,57(7):589-598
Let m and n denote a pair of positive integers. In this paper, we call upon the Hadamard product and computer algebra techniques to evaluate the Fejér integral π ?1 ∫0 π (sin mθ / sin θ) 2n dθ. Using symmetry arguments, it is proved that the value of this integral is an odd polynomial in m of degree 2n ? 1. This permits using polynomial curve fitting methods and mathematical software packages to obtain evaluation formulas for n relatively small. Some cases of the above integral with 2n replaced by 2n + 1 are also discussed. A familiar identity shows that these yield evaluations of integrals of powers of certain Tchebychev polynomials. 相似文献
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Получены асимптотич еские равенства для в еличин гдеr≧0 — целое, ω(t) — выпу клый модуль непрерыв ности и $$\bar \sigma _n (f;x) = - \frac{1}{\pi } \mathop \smallint \limits_{ - \pi }^\pi f(x + t)\left( {\frac{1}{2}ctg\frac{t}{2} - \frac{1}{{4(n + 1)}}\frac{{\sin (n + 1)t}}{{\sin ^2 \tfrac{1}{2}t}}} \right)dt$$ сумма Фейера функцииf(х), сопряженной сf(x). 相似文献
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The Fejér sums of periodic measures and the norms of the deviations from the limit in the von Neumann ergodic theorem are calculating in terms of corresponding Fourier coefficients, in fact, using the same formulas. As a result, well-known estimates for the rates of convergence in the von Neumann ergodic theorem can be restated as estimates for the Fejér sums at a point for periodic measures. In this way, natural sufficient conditions for the polynomial growth and polynomial decay of these sums can be obtained in terms of Fourier coefficients. Besides, for example, it is shown that every continuous 2π-periodic function is uniquely determined by its sequence of Fejér sums at any two points whose difference is incommensurable with π. 相似文献
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Jim Agler Zinaida A. Lykova N.J. Young 《Journal of Mathematical Analysis and Applications》2012,386(1):308-318
We give a new solvability criterion for the boundary Carathéodory–Fejér problem: given a point and, a finite set of target values , to construct a function f in the Pick class such that the limit of as nontangentially in the upper half-plane is for . The criterion is in terms of positivity of an associated Hankel matrix. The proof is based on a reduction method due to Julia and Nevanlinna. 相似文献
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We consider the C*-algebra generated by multidimensional integral operators with (?n)th-order homogeneous kernels and by the operators of multiplication by oscillating coefficients of the form |x|iα. For this algebra, we construct an operator symbolic calculus and obtain necessary and sufficient conditions for the Fredholm property of an operator in terms of this calculus. 相似文献
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The solutions of the Carathéodory–Fejér interpolation problem for generalized Schur functions can be parametrized via a linear fractional transformation over the class of classical Schur functions. The linear fractional transformation of some of these functions may have a pole (simple or multiple) in one or more of the interpolation points or not satisfy one or more interpolation conditions, hence not all Schur functions can serve as a parameter. The set of excluded parameters is characterized in terms of the related Pick matrix.Research was supported by the Summer Research Grant from the College of William and MarySubmitted: June 26, 2002 Revised: January 31, 2003 相似文献
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Zhi-Wei Sun 《Journal of Number Theory》2012,132(11):2673-2699
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Rodolfo Toledo 《Journal of Mathematical Analysis and Applications》2018,457(1):153-178
In this paper we establish an iteration for the -norm of Walsh–Fejér kernels with the assumption that the Walsh functions are ordered in Paley's sense. We use this iteration to prove some properties of this sequence, including that its supremum is exactly equal to . 相似文献
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Ágota P. Horváth 《Acta Mathematica Hungarica》2013,141(4):366-382
We indicate the connections among the Fekete set, the zeros of orthogonal polynomials, 1(w)-normal point systems, and the nodes of an interpolatory process which is called stable and the most economical, via the Fejér constants. Finally the convergence of a weighted Grünwald interpolation is proved. 相似文献
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In this paper we prove that there are operators in the uniform Roe algebra ${C_u^*(G)}$ which cannot be approximated by the truncations of themselves, where G is a finitely generated group. We also give a sufficient condition for the operators which can be approximated by the truncations of themselves. For a countable discrete metric space X, we obtain the similar conclusions. 相似文献
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A. S. Fedorenko 《Ukrainian Mathematical Journal》1999,51(12):1945-1949
We obtain estimates exact in order for the best trigonometric and orthogonal trigonometric approximations of the classesL Ψβ,ρ of functions of one variable in the spaceL q in the case 2<p <q < ∞. 相似文献