Hermitizable, Isospectral Matrices or Differential Operators

Abstract

This paper reports the study on Hermitizable problem for complex matrix or second order differential operator. That is the existence and construction of a positive measure such that the operator becomes Hermitian on the space of complex square-integrable functions with respect to the measure. In which case, the spectrum are real, and the corresponding isospectral matrix/differntial operators are described. The problems have a deep connection to computational mathematics, stochastics, and quantum mechanics.