共查询到20条相似文献,搜索用时 15 毫秒
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I. Yu. Trushin 《Mathematical Notes》1993,54(3):951-956
Translated from Matematicheskie Zametki, Vol. 54, No. 3, pp. 114–122, September, 1993. 相似文献
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Jaak Peetre 《Mathematische Annalen》1967,169(2):307-314
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Mark A. Pinsky 《纯数学与应用数学通讯》1994,47(5):653-681
Necessary and sufficient conditions are found for the convergence at a pre-assigned point of the spherical partial sums (resp. integrals) of the Fourier series (resp. integral) in the class of piecewise smooth functions on Euclidean space. These results carry over unchanged to spherical harmonic expansions, Fourier transforms on hyperbolic space, and Dirichlet eigenfunction expansions with respect to the Laplace operator on a class of Riemannian manifolds. © 1994 John Wiley & Sons, Inc. 相似文献
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We state a localization principle for expansions in eigenfunctions of a self-adjoint second order elliptic operator and we prove an equiconvergence result between eigenfunction expansions and trigonometric expansions. We then study the Gibbs phenomenon for eigenfunction expansions of piecewise smooth functions on two-dimensional manifolds. 相似文献
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I. Joó 《Acta Mathematica Hungarica》1992,60(1-2):125-156
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Leonardo Colzani 《Milan Journal of Mathematics》1988,58(1):149-167
Let {λ 2} and {? λ } be the eigenvalues and an orthonormal system of eigenvectors of a second order elliptic differential operator Δ on a compact manifoldM of dimensionN. We prove that the Riesz means of order δ, defined by \(R_\Lambda ^\delta f = \sum\limits_{\lambda< \Lambda } {\left( {1 - \frac{{\lambda ^2 }}{{\Lambda ^2 }}} \right)^\delta \hat f(} \lambda ) \varphi _\lambda \) , are uniformly bounded from the Hardy spaceH p (M) into Weak-L p (M), if 0<p<1 and δ=N/p?(N+1)/2. 相似文献
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Tassilo Küpper 《Numerische Mathematik》1976,27(1):111-119
Summary For a differential operatorL as defined in (2.1) we consider the eigenvalue problemL u=u and describe a method to obtain a pointwise bound |u–v| wherev denotes the Rayleigh-Ritz approximation to an exact eigenfunctionu. The upper bound is continuous, but only piecewise differentiable and calculated by solving certain (inverse-positive!) auxiliary problems.Our method uses well-known estimations for (t
i) at a finite number of pointst
i[a, b] to calculate an upper, bound in the whole interval [a, b].The author would like to, thank the Battelle Institute Geneve for their assistance 相似文献
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In this paper, for expansions in eigenfunctions and associated functions, an analog of the known A. Zygmund theorem on the
absolute convergence of trigonometric Fourier series is proved.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal
Conference-2004, Part 1, 2005. 相似文献
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V. V. Kornev 《Mathematical Notes》2007,81(5-6):638-648
An analog of Szasz’s theorem on the absolute convergence of trigonometric Fourier series is established for expansions in the eigen and associated functions of integral operators some of whose kernels involve derivatives with discontinuities on the diagonals. 相似文献
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F. Schipp 《Analysis Mathematica》1976,2(1):65-76
- , - n An-,. , . , ¦n¦=1 (n=1,2, ), . , — — , . 相似文献
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Ahmed I. Zayed 《Proceedings of the American Mathematical Society》2000,128(12):3629-3637
Non-orthogonal wavelet expansions associated with a class of mother wavelets is considered. This class of wavelets comprises mother wavelets that are not necessarily integrable over the whole real line, such as Shannon's wavelet. The pointwise convergence of these wavelet expansions is investigated. It is shown that, unlike other wavelet expansions, the ones under consideration do not necessarily converge pointwise to the functions at points of continuity, unless a more stringent condition, such as bounded variation, is imposed.