Results 11 to 20 of about 3,646,213 (202)
Some properties of Riesz means and spectral expansions [PDF]
Electronic Journal of Differential Equations, 1999 It is well known that short-time expansions of heat kernels correlate to formal high-frequency expansions of spectral densities. It is also well known that the latter expansions are generally not literally true beyond the first term.
S. A. Fulling, R. A. Gustafson
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Weighted decoupling estimates and the Bochner-Riesz means [PDF]
Forum of Mathematics, SigmaWe prove new weighted decoupling estimates. As an application, we give an improved sufficient condition for almost everywhere convergence of the Bochner-Riesz means of arbitrary $L^p$ functions for ...
Jongchon Kim
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The Variational Structure of Riesz Means
We establish the variational structure of Riesz means of negative eigenvalues of Schrödinger operators. For Hₕ(y) = −h²Δ − y(x) on L²(ℝᵈ), with negative eigenvalues λₙ = −κₙ² and L²-normalised eigenfunctions ψₙ, the Hellmann–Feynman theorem and the chain rule yield, for every Riesz order γ > ½, the functional identityδ/δy(x) ∑ₙ κₙ^(2γ) = γ ∑ₙ κₙ^(2γ−
Guir, Abdelbaki +1 more
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Some inequalities related to strong convergence of Riesz logarithmic means
Journal of Inequalities and Applications, 2020 In this paper we derive a new strong convergence theorem of Riesz logarithmic means of the one-dimensional Vilenkin–Fourier (Walsh–Fourier) series. The corresponding inequality is pointed out and it is also proved that the inequality is in a sense sharp,
D. Lukkassen +3 more
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On the Hyperbolic Riesz Means [PDF]
Proceedings of the American Mathematical Society, 1983 We define the hyperbolic Riesz means in R
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Fractional variational problems with the Riesz-Caputo derivative [PDF]
, 2012 In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the ...
Almeida, R. +2 more
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A class of fractional Ornstein–Uhlenbeck processes mixed with a Gamma distribution
Modern Stochastics: Theory and Applications, 2022 We consider a sequence of fractional Ornstein–Uhlenbeck processes, that are defined as solutions of a family of stochastic Volterra equations with a kernel given by the Riesz derivative kernel, and leading coefficients given by a sequence of independent ...
Luigi Amedeo Bianchi +2 more
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The Bochner–Riesz means for Fourier–Bessel expansions [PDF]
, 2005 The Bochner–Riesz means for Fourier–Bessel expansions are analyzed. We prove a uniform two-weight inequality, with potential weights, for these means. The result provides necessary and sufficient conditions for boundedness.
Luz Roncal +5 more
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Mathematics, 2019 In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ -Riesz-Caputo fractional derivative. A new definition of ψ -Riesz-Caputo fractional derivative of order
Dandan Yang, Chuanzhi Bai
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On the Riesz means of δ k (n) [PDF]
Hardy-Ramanujan Journal, 2018 Let k ≥ 1 be an integer. Let δ k (n) denote the maximum divisor of n which is co-prime to k. We study the error term of the general m-th Riesz mean of the arithmetical function δ k (n) for any positive integer m ≥ 1, namely the error term E m,k (x) where 1 m! n≤x δ k (n) 1 − n x m = M m,k (x) + E m,k (x).
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