A remark on decay rates of odd partitions: An application of spectral asymptotics of the Neumann--Poincar\'e operators

Abstract

We introduce a theorem currently proved unique by the asymptotic behaviors of eigenvalues of a compact operator. Specifically, a problem of partitions is considered and the Neumann--Poincar\'e operator is employed as the compact linear operator. Then a theorem is proved by the spectrum of the Neumann--Poincar\'e operator.