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Journal of Theoretical Probability

, Volume 22, Issue 1, pp 123–145 | Cite as

A Study of Probability Measures Through Commutators

  • Aurel I. Stan
  • John J. Whitaker
Article

Abstract

The first-order moments and two families of commutators are proven to determine uniquely the moments of a probability measure on ℝ d . These families are the commutators between the annihilation and creation operators, and the commutators between the annihilation and preservation operators. An explicit method for recovering the moments from these commutators and first-order moments is presented.

Keywords

Commutator Annihilation operator Creation operator Preservation operator 

Mathematics Subject Classification (2000)

05E35 60H40 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State University at MarionMarionUSA
  2. 2.Department of Mathematical SciencesShawnee State UniversityPortsmouthUSA

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