Discrete and Cantor Spectrum for Neumann Laplacians of Combs

Extending results of HSS] on the construction of Neumann Laplacians of combs with given essential spectrum S = S 0,∞], we show that, in addition to the essential spectrum, a bounded sequence of discrete eigenvalues can be prescribed. More generally, we find that certain types of spectra can be constructed precisely, in a bounded interval 0, s].