共查询到20条相似文献,搜索用时 15 毫秒
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R. R. Ashurov 《Differential Equations》2008,44(9):1197-1202
For piecewise smooth functions of n variables, we prove the uniform Riesz summability of order s > (n ? 3)/2 of their spectral expansions associated with an arbitrary elliptic operator with constant coefficients. For s = (n ? 3)/2, the corresponding Riesz means are bounded. 相似文献
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Sh. A. Alimov 《Differential Equations》2010,46(6):827-839
We consider the expansion of a piecewise smooth function depending on the geodesic distance to some point in the eigenfunctions
of the Beltrami-Laplace operator on an n-dimensional symmetric space of rank 1. We show that if the expansion converges at this point, then the function must have
continuous derivatives up to and including the order (n − 3)/2. 相似文献
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Rémi Soufflet 《Bulletin of the Brazilian Mathematical Society》2002,33(1):125-146
The aim of this paper is to study the asymptotic expansion of real functions which are finite compositions of globally subanalytic
maps with the exponential function and the logarithmic function. This is done thanks to a preparation theorem in the spirit
of those that exist for analytic functions (Weierstrass) or subanalytic functions (Parusinśki). The main consequence is that
logarithmic-exponential functions admit convergent asymptotic expansion in the scale of real power functions. We also deduce
a partial answer to a conjecture of van den Dries and Miller.
Received: 19 March 2002 相似文献
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J.D Buckholtz 《Journal of Mathematical Analysis and Applications》1973,41(3):673-684
Many of the classical polynomial expansions of analytic functions share a common property: the space of “expandable” functions is a Banach space isometrically isomorphic to the space of complex sequences with limit 0. Under the isometries, these polynomial expansions all correspond to essentially the same biorthogonal expansion in this sequence space. Sufficient conditions for such an isometry to exist are obtained, and convergence properties of the expansions are studied. The results obtained also apply to expansions other than polynomial expansions. 相似文献
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Yu. A. Brychkov 《Mathematical Notes》1972,12(2):513-517
The definition is formulated of the asymptotic expansion of a generalized function depending on a parameter. A number of theorems are proved about the properties of asymptotic expansions and operations on them, in particular, theorems on differentiation and integration. For generalized functions of the formf (x)eixt,f (x) S', t ± the relation is investigated between the singularity carrierf and the carrier of coefficient functionals.Translated from Matematicheskie Zametki, Vol. 12, No. 2, pp. 131–138, August, 1972. 相似文献
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The number of spanning trees in a class of directed circulant graphs with generators depending linearly on the number of vertices \(\beta n\), and in the nth and \((n-1)\)th power graphs of the \(\beta n\)-cycle are evaluated as a product of \(\lceil \beta /2\rceil -1\) terms. 相似文献
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Mourad E.H Ismail Thanaa M.T Rashed 《Journal of Mathematical Analysis and Applications》1977,57(3):724-731
We study expansions in polynomials {Pn(x)}∞o generated by ∑∞n = oPn(x)tn = A(t) φ(xtkθ(t)), θ(0) ≠ 0, and ∑∞n = 0Pn(x)tn = ∑kj = 1Aj(t) φ(xt?j), ?1,…,?k being the k roots of unity. The case k = 1 is contained in a recent work by Fields and Ismail. We also prove a new generalization of Vandermond's inverse relations. 相似文献
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Hyperasymptotic expansions were recently introduced by Berryand Howls, and yield refined information by expanding remaindersin asymptotic expansions. This paper gives a new method forobtaining hyperasymptotic expansions for integrals representingthe confluent hypergeometric U-function. At each level, theremainder is exponentially small compared with the previousremainders, and the number of new terms is increasing. Threenumerical illustrations confirm these exponential improvements. 相似文献
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This paper proposes an extension of the expansions of analytic functions in the An polynomials defined by Adomian [1] to consider piecewise-differentiable functions. 相似文献
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José L. Ló pez Nico M. Temme 《Transactions of the American Mathematical Society》2004,356(11):4323-4342
Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals. The method is also used for obtaining Laurent expansions in several points as well as Taylor-Laurent expansions.
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Jürgen Spilker 《Archiv der Mathematik》1980,35(1):451-453
Using a functional analytic idea, I will show that every bounded arithmetic function possesses a Ramanujan expansion which is pointwise absolutely convergent.Dedicated to Martin Barner on the occasion of his 60th birthday 相似文献
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We study a class of quadratic p-ary functions ${{\mathcal{F}}_{p,n}}$ from ${\mathbb{F}_{p^n}}$ to ${\mathbb{F}_p, p \geq 2}$ , which are well-known to have plateaued Walsh spectrum; i.e., for each ${b \in \mathbb{F}_{p^n}}$ the Walsh transform ${\hat{f}(b)}$ satisfies ${|\hat{f}(b)|^2 \in \{ 0, p^{(n+s)}\}}$ for some integer 0 ≤ s ≤ n ? 1. For various types of integers n, we determine possible values of s, construct ${{\mathcal{F}}_{p,n}}$ with prescribed spectrum, and present enumeration results. Our work generalizes some of the earlier results, in characteristic two, of Khoo et. al. (Des Codes Cryptogr, 38, 279–295, 2006) and Charpin et al. (IEEE Trans Inf Theory 51, 4286–4298, 2005) on semi-bent functions, and of Fitzgerald (Finite Fields Appl 15, 69–81, 2009) on quadratic forms. 相似文献
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I. S. Lomov 《Differential Equations》2014,50(8):1070-1079
We study the convergence rate of biorthogonal series expansions of functions in systems of root functions of a broad class of loaded even-order differential operators defined on a finite interval. These expansions are compared with the Fourier trigonometric series expansions of the same functions in an integral metric on any interior compact set of the main interval or on the entire interval. We obtain estimates for the equiconvergence rate of these expansions. 相似文献
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Pedro Catuogno Christian Olivera 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(2):479-493
In this work we introduce an algebra of tempered generalized functions. The tempered distributions are embedded in this algebra via their Hermite expansions. The Fourier transform is naturally extended to this algebra in such a way that the usual relations involving multiplication, convolution and differentiation are valid. Furthermore, we give a generalized Itô formula in this context and some applications to stochastic analysis. 相似文献