Operator integrals and sesquilinear forms

Daniel A. Dubin; Jukka Kiukas; Juha-Pekka Pellonpaa; Kari Ylinen

doi:10.1016/j.jmaa.2013.11.045

Operator integrals and sesquilinear forms

Daniel A. Dubin, Jukka Kiukas, Juha-Pekka Pellonpaa, Kari Ylinen

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	250–268
Number of pages	19
Journal	Journal of Mathematical Analysis and Applications
Volume	413
Issue number	1
Early online date	25 Nov 2013
DOIs	https://doi.org/10.1016/j.jmaa.2013.11.045
Publication status	Published - 01 May 2014
Externally published	Yes

Keywords

vector measure
operator measure
operator integral
sesquilinear form
quantum observable
Operator measure
Operator integral
Quantum observable
Vector measure
Sesquilinear form

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abstract = "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",

keywords = "vector measure, operator measure, operator integral, sesquilinear form, quantum observable, Operator measure, Operator integral, Quantum observable, Vector measure, Sesquilinear form",

author = "Dubin, {Daniel A.} and Jukka Kiukas and Juha-Pekka Pellonpaa and Kari Ylinen",

note = "Funding Information: We acknowledge financial support from the CHIST-ERA/BMBF project CQC, and the Academy of Finland grant No. 138135 .",

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AU - Dubin, Daniel A.

AU - Kiukas, Jukka

AU - Pellonpaa, Juha-Pekka

AU - Ylinen, Kari

N1 - Funding Information: We acknowledge financial support from the CHIST-ERA/BMBF project CQC, and the Academy of Finland grant No. 138135 .

PY - 2014/5/1

Y1 - 2014/5/1

N2 - 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

AB - 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

KW - vector measure

KW - operator measure

KW - operator integral

KW - sesquilinear form

KW - quantum observable

KW - Operator measure

KW - Operator integral

KW - Quantum observable

KW - Vector measure

KW - Sesquilinear form

UR - http://hdl.handle.net/2160/43640

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DO - 10.1016/j.jmaa.2013.11.045

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SN - 0022-247X

VL - 413

SP - 250

EP - 268

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Operator integrals and sesquilinear forms

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Keywords

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