Generalized uncertainty principles on spaces of homogeneous type
The author presents a generalized version of Weyl's law and the Heisenberg uncertainty principle on connected spaces of homogeneous type with finite volume (e.g. Riemannian manifolds or fractals as well). Theorems proved in this interesting paper establish a correspondence between the geometry and spectral properties of some model positive operator \(D_\varepsilon\), a substitute for \((- \Delta)^{\varepsilon/2}\) on compact manifolds, and the geometry of its underlying space. Here \(\varepsilon\) is a sufficiently small positive number.
scientific article; zbMATH DE number 599828