Results 141 to 150 of about 27,509 (180)

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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Riesz Mean-Value Theorem Extended

1983
The mean-value theorem of M. Riesz is valid only for exponents in the range (−1,0]. It is here shown that the theorem can be extended to greater exponents in a modified form by introducing adequate factors which yield a positivity property. Several directions for applications are indicated.
H. Türke, K. Zeller
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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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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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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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Inclusion Relations for General Riesz Typical Means

Canadian Mathematical Bulletin, 1974
Let α be a non-negative real number, λ≡{λ,n}(n≥0) a strictly increasing unbounded sequence with λ0≥0 and let be an arbitrary series with partial sums s≡{sn}. Writewhere s(t)=sn for λn<t≤λn+1, s(t)=0 for 0≤t≤λ0. The series ∑ an or the sequence of partial sums s={sn} is summable to ṡ by the Riesz method (R, λ, α) ifas ω→∞.
Jakimovski, A., Tzimbalario, J.
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A note on Riesz means

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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Inclusion relations for Riesz typical means

Mathematical Proceedings of the Cambridge Philosophical Society, 1972
AbstractNecessary and sufficient conditions for sequence-to-sequence or sequence-to-function summability method to include (R, λ, α), when 1 < α ≤ 2, are given. Also, for suitably restricted sequences λ, necessary and sufficient conditions for a series-to-sequence or series-to-function summability method to include (R, λ, α) for 1 < α ≤ 2 are ...
Jakimovski, A., Tzimbalario, J.
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Riesz Means on Compact Riemannian Symmetric Spaces

Mathematische Nachrichten, 1994
AbstractWe study approximation properties of the Riesz means on compact symmetric spaces of rank one. To do so we establish equivalences between the Riesz means and Peetre K‐moduli and estimate the weak type and the uniform approximation of the Riesz means at the critical index.
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The Riesz Mean Ergodic Theorem

2019
If T is a non-expansive linear map of a uniformly convex Banach space, then all the fixed points of T are recovered by means of a limit procedure.
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