18 citations · 24 across the 4 of their papers we have counts for
4 papers
On Harrell-Stubbe Type Inequalities for the Discrete Spectrum of a Self-Adjoint Operator
Mark S. Ashbaugh, Lotfi Hermi
We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleig…
On Riesz Means of Eigenvalues
Evans M. Harrell, Lotfi Hermi
In this article we prove the equivalence of certain inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian with a classical inequality of Kac. Connections are made…
Two new Weyl-type bounds for the Dirichlet Laplacian
Lotfi Hermi
In this paper, we prove two new Weyl-type upper estimates for the eigenvalues of the Dirichlet Laplacian. As a consequence, we obtain the following {\em lower} bounds for its count…
Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues
Evans M. Harrell, Lotfi Hermi
We derive differential inequalities and difference inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian, R_σ(z) := \sum_k{(z -λ_k)_+^σ}. Here ${λ_k}_{k=1}^{\infty…