Growth and spectrum of diffusions
We prove an upper bound on the bottom of the essential spectrum of a diffusion in term of the growth of the volume of $X$, generalizing a result by R. Brooks.
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arXiv subjects
Lino Notarantonio
Publications and source records attributed to Lino Notarantonio.
Spectrum of compact manifolds with high genus
In this paper we study the behavior of the spectrum of a compact, connected Riemannian manifold $(M,g)$ of dimension $d \ge 2$, when we add an increasing number of increasingly small handles. No assumptions on any of the curvatures are needed.
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Extremal properties of the first eigenvalue of Schrödinger-type operators
Given a separable, locally compact Hausdorff space $X$ and a positive Radon measure $m(dx)$ on it, we study the problem of finding the potential $V(x) \ge 0$ that maximizes the first eigenvalue of the Schrödinger-type operator $L+V(x)$; $L$ is the generator of a local Dirichlet form $(a, D[a])$ on $L^2(X, m(dx))$.
math.SP↗