Bargmann representation of q-commutation relations for q > 1 and associated measures

• Autorzy: Ilona Królak
• Języki publikacji: EN

Abstrakty

EN

The classical Bargmann representation is given by operators acting on the space of holomorphic functions with the scalar product $⟨zⁿ|z^k⟩_q = δ_{n,k}[n]_q! = F(zⁿz̅^k)$. We consider the problem of representing the functional F as a measure for q > 1. We prove the existence of such a measure and investigate some of its properties like uniqueness and radiality. The above problem is closely related to the indeterminate Stieltjes moment problem.

Kategorie tematyczne

• 81S05: Canonical quantization, commutation relations and statistics
• 30E05: Moment problems, interpolation problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 78
• Numer: 1
• Strony: 171-183

Daty

wydano

2007

Twórcy

autor

Ilona Królak

• Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/bc78-0-13