The following is a discussion regarding a specific set of operators acting on the space of functions analytic on the unit disk. A diagonal operator is said to admit spectral synthesis if all of its invariant subspaces can be expressed as a closed linear span of a subset of its eigenvectors. This article employs various techniques for verifying the convergence of infinite products and infinite sums as a means of demonstrating that a certain class of operators fail to admit spectral synthesis.
"An Application of Infinite Sums and Products Relating to Spectral Synthesis." Missouri J. Math. Sci. 31 (1) 1 - 13, May 2019. https://doi.org/10.35834/mjms/1559181622