We consider a “convolution mm-Laplacian” operator on metric-measure spaces and study its spectral properties. The definition is based on averaging over small metric balls. For reasonably nice metric-measure spaces we prove stability of convolution Laplacian’s spectrum with respect to metric-measure perturbations and obtain Weyl-type estimates on the number of eigenvalues.
|Original language||English (US)|
|Number of pages||34|
|Journal||Israel Journal of Mathematics|
|State||Published - Aug 1 2019|
All Science Journal Classification (ASJC) codes