Laplacian eigenspace ($E_{\lambda }=\ker (\Delta -\lambda I)$)

The vector space of functions satisfying $\Delta f=\lambda f$ for a specified Laplace-Beltrami operator. On a closed manifold its dimension is finite and is the spectral multiplicity of $\lambda$. A finite isometric group action preserves this space; invariant elements are the Laplacian eigenfunctions on the corresponding smooth quotient.