Results 161 to 170 of about 3,646,213 (202)

Riesz Means on Graphs and Discrete Groups

Potential Analysis, 2011
For \(\alpha>0\) and \(R>0\), the Riesz mean of order \(\alpha\) is the operator defined by \[ m_{\alpha,R}(\Delta) = \int_0^2 m_{\alpha,R}(\lambda) \mathrm{d}E_\lambda \] where \(\Delta\) is the discrete Laplacian, \(\mathrm{d}E_\lambda\) is its spectral measure (so that \(\Delta = \int_0^2 \lambda \mathrm{d}E_\lambda\)) and \[ m_{\alpha,R}(\lambda) =
Fotiadis, Anestis, Georgiadis, Athanasios G.   +1 more
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Semi-Classical Asymptotics of Riesz Means

Journal of the London Mathematical Society, 2000
Summary: 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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Poincaré Rotation Numbers and the Riesz and Voronoi Means

Mathematical Notes, 2003
We 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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Twisted convolution and Riesz means

Journal d'Analyse Mathématique, 1998
Using 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 the equiconvergence of the riesz means with exact order

Acta Mathematica Hungarica, 1991
In 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 Convergence of Riesz Means on Compact Manifolds

The Annals of Mathematics, 1987
Let 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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On the Riesz Means of Expansions by Riesz Bases Formed by Eigenfunctions of the Schrödinger Operator

Periodica Mathematica Hungarica, 1987
The 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

1987
This 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, Yang-Chun Chang   +1 more
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Strong summability of Riesz means

Mathematical Notes of the Academy of Sciences of the USSR, 1986
Let \(\{u_ n(x)\}\) 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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A note on Riesz and Nörlund means

Rendiconti del Circolo Matematico di Palermo, 1969
In a previous paper [3], the author has considered the necessary and sufficient conditions in order that (R, λn, 1)→(N, pn) and |R, λn, 1|→|N, pn|. In the present note in §2, necessary and sufficient conditions in order that (N, pn)→(R, λn, 1) and |N, pn|→|R, λn, 1|, have been discussed.
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