Results 151 to 160 of about 863 (193)
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Semi-Classical Asymptotics of Riesz Means
Journal of the London Mathematical Society, 2000Summary: The semi-classical asymptotic behaviour of the Riesz means of a distribution of eigenvalues is investigated at a non-critical energy level. For Schrödinger type operators, the second term related to the periodic trajectories of the classical Hamiltonian is obtained.
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Mathematical Proceedings of the Cambridge Philosophical Society, 1968
1. For the familiar definition of (R, λn, κ), (R*, λn, κ) and (N, p) means and their notations, see, for example (3). If {fn} is any arbitrary sequence, we adopt the convention throughout that f−1 = 0. A method of absolute summability |A| is said to be ineffective if it is absolutely regular and sums only absolutely convergent sequences.
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1. For the familiar definition of (R, λn, κ), (R*, λn, κ) and (N, p) means and their notations, see, for example (3). If {fn} is any arbitrary sequence, we adopt the convention throughout that f−1 = 0. A method of absolute summability |A| is said to be ineffective if it is absolutely regular and sums only absolutely convergent sequences.
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Twisted convolution and Riesz means
Journal d'Analyse Mathématique, 1998Using some estimates of Askey and Wainger for Laguerre functions, the authors improve a result in [\textit{S. Thangavelu}, Ark. Mat. 29, No. 2, 307-321 (1991; Zbl 0765.42009)]. Consider the twisted Laplacian on \(\mathbb{R}^{2n}\), \(n\geq 1\), \[ -\Delta_x- \Delta_y+ 1/4(| x|^2+| y|^2)- i \sum^n_{j=1} \Biggl(x_j{\partial\over\partial y_j}- y_j ...
Stempak, Krzysztof, Zienkiewicz, Jacek
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On Abel—Poisson type and Riesz means
Analysis Mathematica, 1981В работе исследуются ядра методов суммиро вания типа Абеля—Пуассона и Рис са, применяемых к кратны м интегралам Фурье. Вы ясняются условия на параметры, определяющие эти методы, при которы х их ядра неотрицател ьны. Полученные результа ты можно сформулировать в тер минах положительной определенности неко торых функций.
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On the Convergence of Riesz Means on Compact Manifolds
The Annals of Mathematics, 1987Let M be a compact connected \(C^{\infty}\) manifold of dimension \(n\geq 2\) and P an elliptic differential operator on M with \(C^{\infty}\) coefficients and self-adjoint with respect to some positive \(C^{\infty}\) density dx, i.e. in the Lebesgue space \(L^ 2(M)\) associated with dx. Then \(L^ 2(M)\) has the direct sum decomposition \(L^ 2(M)=\sum^{
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Poincaré Rotation Numbers and the Riesz and Voronoi Means
Mathematical Notes, 2003We say that a sequence of numbers (not necessarily converging) converges in Cesàro sense, if their averages converge. We say that it converges in the sense of Riesz with given weights \(p_0, p_1,\dots\), \(p_0>0\), \(p_i\geq0\), if their averages with the weights \(p_i\) converge.
Kozlov, V.V., Madsen, Tatiana Kozlova
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On the equiconvergence of the riesz means with exact order
Acta Mathematica Hungarica, 1991In the present paper we prove an equiconvergence of the Riesz means with exact order for functions with given integral modulus of continuity. Our proof is a synthesis which is based on a fruitful method of V. A. Il'in.
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On the Riesz Means of Expansions by Riesz Bases Formed by Eigenfunctions of the Schrödinger Operator
Periodica Mathematica Hungarica, 1987The author proves a result on the convergence of Riesz means of expansions with respect to Riesz bases \(\{u_ k\}\) of \(\sigma_ k\)-th order eigenfunctions of a nonself-adjoint one-dimensional Schrödinger operator on a bounded interval. The result extends earlier results of \textit{I. Joó} and \textit{V. Komornik} [Acta. Sci. Math.
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Lectures on Bochner-Riesz Means
1987This book is concerned with the modern theory of Fourier series. Treating developments since Zygmund's classic study, the authors begin with a thorough discussion of the classical one-dimensional theory from a modern perspective. The text then takes up the developments of the 1970s, beginning with Fefferman's famous disc counterexample. The culminating
Katherine Michelle Davis +1 more
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Strong summability of Riesz means
Mathematical Notes of the Academy of Sciences of the USSR, 1986Let \(\{u_ n(x)\}\) be a complete orthonormalized system of eigenfunctions of the self-adjoint extension of Laplace operator - \(\Delta\) in N-dimensional domain \(\Omega\) with discrete spectrum, and let \(\lambda_ n=\mu_ n^ 2\) be the corresponding eigenvalues numbered in increasing order.
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