A note on the Weyl formula for balls in $\mathbb{R}^d$

Abstract

Let B = {x ∈ R d : |x| < R} (d ≥ 3) be a ball. We consider the Dirichlet Laplacian associated with B and prove that its eigenvalue counting function has an asymptotics18627 8320 ä as µ → ∞.