Let \(\mathcal{D}'(\mathbb{R}^n)\) and \(\mathcal{E}'(\mathbb{R}^n)\) be the spaces of distributions compactly supported on \(\mathbb{R}^n\), \(n\geq 2\) respectively, let \(\mathcal{E}'_{\natural}(\mathbb{R}^n)\) space all radial (invariant under rotations \(mathbb{R}^n\)) in \(\mathcal{E}'(\mathbb{R}^n)\), let\(\widetilde{T}\) spherical transform (Fourier–Bessel transform) a distribution \(T\...

SFB393/05-01 January 2005 Abstract The Laplace-Beltrami operator corresponds to the Laplace operator on curved surfaces. In this paper, we consider an eigenvalue problem for the Laplace-Beltrami operator on subdomains of the unit sphere in R. We develop a residual a posteriori error estimator for the eigenpairs and derive a reliable estimate for the eigenvalues. A global parametrization of the ...