We discuss the division method for subspectra which appears to be one of the key approaches in the study of spectral properties of self-adjoint differential vector-operators, that is operators generated as a direct sum of self-adjoint extensions on an Everitt-Markus-Zettl multi-interval system. In the current work we show how the division method may be applied to obtain the ordered spectral rep...

— In this work we extend a previous work about the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint differential operators with small multiplicative random perturbations, by treating the case of operators on compact manifolds.

The norm convergence of the Trotter{Kato product formula is established with ultimate optimal error bound for the self-adjoint semigroup generated by the operator sum of two self-adjoint operators. A generalization is also given to the operator sum of several self-adjoint operators.