Rank-deficient spectral factorization and wavelets completion problem

A simple constructive proof of polynomial matrix spectral factorization theorem is presented in the rank-deficient case. It is then used to provide an elementary solution to the wavelets completion problem.

FINITE IDEMPOTENT INVERSE MONOID PRESENTATIONS

Several decidability problems for finite idempotent presentations of inverse monoids are solved, giving also insight into their structure. Besides providing a new elementary solution for the problem, solutions are obtained for the following problems: computing the maximal subgroups, being combinatorial, being semisimple, being fundamental, having infinite [Formula: see text]-classes. The word problem for the least fundamental quotient is also solved, with an unexpected consequence.