Operator integrals and sesquilinear forms

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:413

Article

Dubin, D. A.¹  Kiukas, J.²  Pellonpaa, J. P.³  Ylinen, K.⁴ 

[1] Open Univ, Dept Pure Math, Milton Keynes MK7 6AA, Bucks, England

[2] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

[3] Univ Turku, Dept Phys & Astron, FI-20014 Turku, Finland

[4] Univ Turku, Dept Math & Stat, FI-20014 Turku, Finland

关键词: Vector measure;    Operator measure;    Operator integral;    Sesquilinear form;    Quantum observable;   

DOI  :  10.1016/j.jmaa.2013.11.045

来源: Elsevier

【 摘 要 】

We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to each other in view of the extension theory of symmetric operators. We demonstrate the associated mathematical subtleties with a physically relevant example involving moment operators of the momentum observable of a particle confined to move on a bounded interval. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free