共查询到20条相似文献,搜索用时 15 毫秒
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M. I. Nagnybida 《Ukrainian Mathematical Journal》1996,48(7):1084-1098
In the space A (θ) of all one-valued functions f(z) analytic in an arbitrary region G ? ? (0 ∈ G) with the topology of compact convergence, we establish necessary and sufficient conditions for the equivalence of the operators L 1=α n z n Δ n + ... + α1 zΔ+α0 E and L 2= z n a n (z)Δ n + ... + za 1(z)Δ+a 0(z)E, where δ: (Δ?)(z)=(f(z)-?(0))/z is the Pommier operator in A(G), n ∈ ?, α n ∈ ?, a k (z) ∈ A(G), 0≤k≤n, and the following condition is satisfied: Σ j=s n?1 α j+1 ∈ 0, s=0,1,...,n?1. We also prove that the operators z s+1Δ+β(z)E, β(z) ∈ A R , s ∈ ?, and z s+1 are equivalent in the spaces A R, 0?R?-∞, if and only if β(z) = 0. 相似文献
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Chen Dirong 《数学学报(英文版)》1994,10(3):315-324
This paper discusses some problems on the cardinal spline interpolation corresponding to infinite order differential operators.
The remainder formulas and a dual theorem are established for some convolution classes, where the kernels arePF densities. Moreover, the exact error of approximation of a convolution class with interpolation cardinal splines is determined.
The exact values of averagen-Kolmogorov widths are obtained for the convolution class.
Supported in part by NSFC. 相似文献
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Youngjoon Cha Haseo Ki Young-One Kim 《Journal of Mathematical Analysis and Applications》2004,290(2):534-541
A sufficient condition for entire functions f and g to be such that the series ∑m=0∞f(m)(0)g(m)/m! represents an entire function is established; and in that case, the growth of the resulting function is described. 相似文献
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Yuri Kozitsky Piotr Oleszczuk 《Journal of Mathematical Analysis and Applications》2003,277(2):423-437
Differential operators ?(Δθ,ω), where ? is an exponential type entire function of a single complex variable and Δθ,ω=(θ+ωz)D+zD2, D=∂/∂z, , θ?0, , acting in the spaces of exponential type entire function are studied. It is shown that, for ω?0, such operators preserve the set of Laguerre entire functions provided the function ? also belongs to this set. The latter consists of the polynomials possessing real nonpositive zeros only and of their uniform limits on compact subsets of the complex plane . The operator exp(aΔθ,ω), a?0 is studied in more details. In particular, it is shown that it preserves the set of Laguerre entire functions for all . An integral representation of exp(aΔθ,ω), a>0 is obtained. These results are used to obtain the solutions to certain Cauchy problems employing Δθ,ω. 相似文献
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Marco Cappiello 《Annali dell'Universita di Ferrara》2002,48(1):75-97
The aim of this work is to study a class of symbols of infinite order and to develop a global calculus for the corresponding
pseudodifferential operators. In particular, we obtain results of boundedness for the operators and of global regularity for
the solutions of the associated equations in the Gelfand spaces.
Sunto Lo scopo di questo lavoro è studiare una classe di simboli di ordine infinito e sviluppare un calcolo globale per gli operatori pseudodifferenziali corrispondenti. In particolare, otteniamo risultati di continuità per gli operatori e di regolarità globale per le soluzioni delle equazioni associate negli spazi di Gelfand.相似文献
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A connection between solutions of an operator equation with Hankel matrices is established.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 998–1000, July, 1990. 相似文献
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Angela A. Albanese 《Proceedings of the American Mathematical Society》2000,128(2):583-588
For coechelon spaces of infinite order it is proved that every compact subset of is contained in a closed absolutely convex hull of some null sequence if and only if the matrix is regularly decreasing.
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Michael Langenbruch 《Journal of Mathematical Analysis and Applications》2004,297(2):696-719
For an open set let A(Ω) be the space of real analytic functions on Ω. Improving our previous results, we prove a new quantitative characterization of the linear partial differential operators P(D) which are surjective on A(Ω). This implies that P(D) is surjective on if P(D) is surjective on A(Ω) for some Ω≠∅. Further inheritance properties for the surjectivity of P(D) on A(Ω) are also obtained. 相似文献