Towards Generalized Riesz Systems Theory
Alan Kamuda, Sergiusz Ku\.zel
TL;DR
This paper analyzes Generalized Riesz Systems (GRS) within basis theory, exploring their properties and relationships with semi-regular sequences, to deepen understanding of their role in pseudo-Hermitian Hamiltonians.
Contribution
It offers new characterizations of GRSs and links them to semi-regular sequences, advancing the theoretical framework of GRSs in basis theory.
Findings
Characterization of GRSs in basis theory
Relationship established between GRSs and semi-regular sequences
Enhanced understanding of GRSs in pseudo-Hermitian Hamiltonians
Abstract
Pseudo-Hermitian Hamiltonians have recently become a field of wide investigation. Originally, the Generalized Riesz Systems (GRS) have been introduced as an auxiliary tool in this theory. In contrast, the current paper, GRSs are analysed in terms of basis theory. The relationship between semi-regular sequences and GRSs is provided. Various characterizations of GRSs are discussed.
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