01230nas a2200157   4500008004100000245009000041210006900131260002100200300001000221490000700231520073600238100001700974700001800991700001301009856005001022       2016                        eng d00aSpectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds0 aSpectral analysis and the AharonovBohm effect on certain almostR  bTaylor & Francis  a32-500 v413 a<p>We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.</p>1 aBoscain, Ugo1 aPrandi, Dario1 aSeri, M.  uhttps://doi.org/10.1080/03605302.2015.1095766