Non-self adjoint Hamiltonian and its applications (Mathematical aspects of quantum fields and related topics)

Abstract

Theory of non-self adjoint operators and these applications are interested in various fields of mathematics and physics. These are many research results related to pseudo-Hermitian operators. In this filed, generalized Riesz systems can be used to construct some physical operators. From this fact, it seems to be important to consider under what conditions biorthogonal sequences are generalized Riesz systems. In this paper, we shall focus introduce the research I have done in the last few years.