This book introduces and discusses the self-adjoint extension problem for symmetric
operators on Hilbert space. It presents the classical von Neumann and Krein–Vishik–Birman …

Two-dimension almost-Riemannian structures of step 2 are natural generalizations of the
Grushin plane. They are generalized Riemannian structures for which the vectors of a local …

We classify the self-adjoint realizations of the Laplace–Beltrami operator minimally defined
on an infinite cylinder equipped with an incomplete Riemannian metric of Grushin type, in …

The heat equation with inverse-square potential on both half-lines of ℝ is discussed in the
presence of bridging boundary conditions at the origin. The problem is the lowest energy …

The study of a quantum particle on degenerate Riemannian manifolds, and the problem of
the purely geometric confinement away from the singularity locus of the metric, as opposite …

O objectivo desta dissertação é apresentar uma fórmula de Chern-Gauss-Bonnet para as
variedades de Grushin. O teorema concebe uma invariante geométrica que conecta …

In this thesis we study some problems of controllability, confinement, and transmission for
the Schroödinger equation for some choices of Riemannian manifolds. We present a …