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math.SP2020★ 1 cited
On the spectrum of the hierarchical Schrödinger type operators
Alexander Bendikov, Alexander Grigor'yan, Stanislav Molchanov
The goal of this paper is the spectral analysis of the Schrödinger type operator , the perturbation of the Taibleson-Vladimirov multiplier by a potential…
math.SP2020
Hierarchical Schrödinger-type operators: the case of potentials with local singularities
Alexander Bendikov, Alexander Grigor'yan, Stanislav Molchanov
The goal of this paper is twofold. We prove that the operator , a perturbation of the Taibleson-Vladimirov multiplier by a potential $V(x)=b\left\Vert x\…
math.SP2010★ 2 cited
Hardy inequality and heat semigroup estimates for Riemannian manifolds with singular data
M. van den Berg, P. Gilkey, K. Kirsten +1
Upper bounds are obtained for the heat content of an open set D in a geodesically complete Riemannian manifold M with Dirichlet boundary condition on bd(D), and non-negative initia…